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AuthorIndexAbel,N.
H.
185Adler,M.
117,126,147,174Akhiezer,N.
l.
177,182,187Alexandrov,A.
D.
5,8Anosov,D.
V.
288Appel,P.
5Arnol'd,V.
I.
8,160,266Baker,H.
F.
177,182,187Baxter,R.
198,219Belavin,A.
A.
126,190,197,219Benjamin,T.
B.
96Berezin,F.
A.
88,119,266Birman,M.
S.
250Bobenko,A.
l.
188,197Bogoyavlensky,0.
1.
114,133,147,174,318Bohr,N.
228Bolsinov,A.
V.
182,302,318,321Bore!
,A.
12Borovik,A.
E.
197Bott,R.
281Brailov,A.
V.
285,291,314,317,322Bruhat,F.
128,131,239Burmistrova,A.
B.
291Calogero,F.
95,96,100,102,114Caratheodory,C.
5,7,35,36Carnot,L.
7,35Casimir,H.
119,128,205,233,238Cartan,E.
5,7,14,15,20,22,39,98,109,128,138,155,161,164,171,174,234,277,324Cauchy,A.
37,106,109,112,247Chaplygin,S.
A.
5,285Cherednik,I.
V.
147,180,197Chernyakov,A.
G.
8,22,45Chevalley,C.
236,243Chow,W.
L.
4,7,35Chudnovsky,D.
V.
175Chudnovsky,G.
V.
175Clebsch,A.
163,174Cousin,J.
192Cristoffel,E.
B.
39,52,54DaoChongTkhi317Dirac,P.
A.
M.
5Drinfel'd,V.
G.
126,197,219Dubrovin,B.
A.
179Duflo,M.
233,238Dynkin,E.
B.
98,139Eliashberg,Ya.
M.
8Euler,L.
8,37,38,154,158,267Faddeev,L.
D.
8,198Filippov,A.
F.
37Finikov,S.
P.
36,39Flaschka,H.
144,133Floquet,G.
56Fomenko,A.
T.
160,182,268,275,282,284-298,304,306,308Fordy,A.
175,319Fourier,J.
H.
S.
176,249Franklin,G.
7Frenkel,I.
B.
126,147Frobenius,G.
4,12,316Fubini,G.
251Fuks,D.
B.
263Galois,E.
V.
246Garnier,R.
172Gel'fand,I.
M.
258Gibbs,J.
W.
5Gindikin,S.
G.
240,258Golod,P.
l.
197Goodman,R.
257Gorbatenko,E.
M.
6Goryachev,D.
N.
285Grassmann,H.
163Griffith,Ph.
4Gromov,M.
263,265Guillemin,V.
155,257,281Haar,A.
68,241Hall,M.
,Jr26Hamilton,W.
R.
88,270Harish-Chandra234,238,241,258Hausdorf,F.
48Heisenberg,W.
23,49Hertz,H.
4,5,7,9Hilbert,D.
269336AuthorIndexHlder,0.
5Hopf,H.
35,36Horak,M.
5Hrmander,L.
5lssaly6Its,A.
R.
179,188lvanov,N.
V.
8lwasawa,H.
130,235,239Jacobi,C.
J.
101,118,120,154,263,270Jacquet,H.
240,258Kac,V.
G.
98,146Kadomtsev,B.
B.
96Kagan,V.
F.
6,36Karasev,M.
V.
154Karpelevich,F.
240,258Kato,T.
250Kawaguchi,A.
36Kazhdan,D.
114,154Kharlamov,M.
P.
285Killing,W.
128,235,308Kirchhoff,P.
269Kirillov,A.
A.
88,119,229,266Klingenberg,W.
288Komarov,I.
V.
174Korteweg,D.
J.
5,269Kostant,B.
114,117,119,126,133,229,231,232Kowalewski,S.
V.
117,167,174,285Kozlov,V.
V.
9Krichever,I.
M.
113,179Lagrange,J.
Z.
16,37,38,117,166Landau,L.
D.
197Langlands,R.
242Laplace,P.
S.
238,249Laptev,G.
F.
22Laurent,P.
A.
99,133Lax,P.
87,100,104,114,117,121,155,250LeNgokT'euen316,317Lebesgue,H.
L.
251,269Legendre,A.
M.
156Leibniz,G.
W.
118,310Levi-Civita,T.
5Lie,S.
87,98,117,119,133,154,234,272,322Lifshitz,E.
M.
197Liouville,J.
91,271,272Liubich,Yu.
I.
8Lobachevsky,N.
l.
6,111Lumiste,Yu.
G.
8Macdonald,H.
M.
250Mackey,G.
W.
155Magri,F.
121,147,220Mamedov,G.
291Manakov,S.
V.
114,133,159,160,306Manin,Yu.
I.
202Marsden,J.
114,154Marshall,I.
175,319Matveev,S.
V.
291Matveev,V.
B.
179,188Maurer,L.
14Meshcheryakov,M.
V.
310Minkowski,H.
46Mishchenko,A.
S.
160,182,268,275,306,308Mittag-LeiDer,G.
188,190Moerbeke,P.
van126,147,174,180Moody,R.
98,146Moore,C.
L.
7Moser,J.
95,114,133,162,174Mumford,D.
126,180Narasimham,M.
265Neumann,C.
162Novikov,S.
P.
155,179,263Ol'shanetsky,M.
A.
114Ono,H.
96Oshemkov,A.
A.
300Perelomov,A.
M.
114,174Petrov,N.
N.
8Petviashvili,V.
l.
96Pfaff,F.
14Plancherel,M.
248,257Pogosyan,T.
I.
285Poincare,H.
315Poisson,S.
D.
88,118,119,148,158,198,231,263Polyakov,A.
M.
155Popov,V.
A.
265Pukanszky,L.
228Ragnisco,0.
174Ramanan,S.
265Rashevsky,P.
K.
4,7,35Ratiu,T.
155,174Rawnsley,J.
H.
155Reyman,A.
G.
126,147,155,160,174,180,182,188,197,257deRham,G.
228,273Riemann,B.
117,122,175,192Rinow,W.
35,36Roch,E.
179Routh,E.
5AuthorIndexSchiffmann,G.
240,254Schmeltzer,I.
155Schmidt,E.
269Schenberg,I.
7Schouten,J.
A.
6Schrdinger,E.
242,250Schwartz,L.
252Semenov-Tian-Shansky,M.
A.
126,147,155,160,174,180,182,188,197,219,257Shcherbakov,V.
N.
8Sinai,Ya.
G.
107Sintsov,D.
M.
6Sklyanin,E.
K.
197,198,201,214,219Sommerfeld,A.
228Souriau,J.
M.
119,155Stckel,P.
271Steklov,V.
A.
196Sternberg,S.
155,257,281Sussmann,H.
J.
36Sutherland,B.
95,100,102,107,114Synge,J.
l.
5,6Takens,F.
288Takhtajan,L.
A.
198Tischler,D.
265Toda,M.
97,102,111,126,141,153,226,234,238Trofimov,V.
V.
269,305,309-312,314,318Thurston,W.
264Uhlenbeck,K.
162Vagner,V.
V.
6,7,36Vassiliev,A.
M.
8Vergne,M.
311,318Vershik,A.
M.
45Veselov,A.
P.
197Vessio,E.
14Vinogradov,A.
M.
8Volterra,V.
5Voronets,P.
V.
5Voss,A.
5Vranceanu,G.
6,8deVries,G.
269Waldhausen,F.
291Wallach,N.
257Weierstrass,C.
87,96Weinstein,A.
114,119,154,220Weyl,H.
6,97,132,159,235,242,250,326Whitney,H.
25Whittaker,E.
238-242,257Wigner,E.
155Witt,E.
27Wojciechowski,S.
174,175,319Yang123Zieschang,H.
291337SubjectIndexAbeltransform185actionfunctional42adjointaction323-representation88,323admissiblecurveforadistribution10--forapolysystem44algorithm(a)314anharmonicoscillator172annihilatorofacovector274Baker-Akhiezerfunction183baseofarootsystem325basisofaregulardistribution17BaxterLiealgebra201bifurcationdiagram282Bohr-Zommerfeldcondition228Bore!
theorem12Bottfunction281Bruhatdecomposition128Carnot-Caratheodorymetric36Cartandecomposition156-matrix98,129,141-subalgebra128,324--,extended138Cartan'stheorem15Casimirfunction119-operator233classofafunctionalsystem277coadjointorbit88,119,265-representation88,119,323codistribution14coflagofaPfaffiansystem15collectivefunction280compactrealform326compactlyembeddedsubalgebra326completelyintegrablesystem271---,collective281---,inthenoncommutativesense275connectionasdistribution21-form21-overadistribution22contactstructure22coordinatesystemcompatiblewithabasis18Couzinproblern145,192Coxeterautomorphism98criticalpoint281-submanifold,nondegenerate281-value281cylinder283degreeofaconnection21-ofnonholonomicity14differentialsystem11diskintheReisenberggroup49dissipativesolidtorus283distribution10-,Cartan20-,completelynonholonomic14-,horizontal21-,integrable10-,involutive11-,ofmaximalgrowth25-,regular14double202dressingtransformation205dualpair148Dufloisomorphism233energyform247-space246equivalenceconjecture276Eulerequations156,267Euler-Lagrangeequations38Euler-Poissonequations158factorizationproblern122Filippov'sIemma37flagmanifold20-ofaconnection21-ofadifferentialsystem13-ofadistribution12flatconnection21Floquettheorem56Frobeniustheorem12functionalequationsforscatteringoperator250--forWhittakerfunctions240functionsininvolution263Garniersystem172gradingofanaffineLiealgebra139principal128,139GrassmannIibration10-manifold163growthdefectofadistribution28-vector14gyrostat166Hamilton-Jacobiproblern271Hamiltonian118,263-,reduced149-groupaction88,148,278-reduction147-subalgebra306-vectorfield118,268Harish-Chandrafunction241-homomorphism238heightofaroot128,139Heisenbergrepresentation189Hopf-Rinowtheorem36,37Hallfamily26Hall-Witttheorem27horosphericalCoordinates111-projection95ideal,differential15-,special15indexofaLiealgebra274inertiatensor155integral263-,Bott282-,complete270-,nonorientable287-,orientable287-form265-submanifold13invariant311Iwasawadecomposition130,235jetofadistribution12-ofavectorfield11Kac-Moodyalgebra98,146kinematicsofarigidbody155Kirillovbracket88,119,266-form88,266Korteweg-deVriesequation269Kawalewskitop167Lagrangemultiplier37-top166Lagrangiansubalgebra227-submanifold270SubjectIndexLanglandsdecomposition242Laxequation87,121Iemmaonquasitriangularform17lengthfunctional36Liealgebra322-,affine133,137-,compact326-,double202-,Frobenius316-,graded126-,nilpotent323-,orthogonalsymmetric327-,selfadjoint316-,semisimple323-,simple323-,solvable323-,withPoincareduality315Liebialgebra200--,factorizable201Liegroup322Lie-Poissonbracket119Lie'stheorem272Iift278linearbundle,regular178Liouville'stheorem272--,noncommutative275loopalgebra133--,twisted133magneticbundle150-form151Manintriple202Maurer-Cartanformula15Mittag-Leffiertheorem189mixedbundle("centaure")16,37momentmap89,148,279monodromymapping57-submanifold62Morsepotential131motionofarigidbodyinfluid,Clebschcase163-------,Steklovcase196multidimensionalrigidbody155-172---,equationsofmotion156,268---,inaquadraticpotential162Neumannsystem162--,inmonopalefield162nilpotentelement327-operator327nonholonomicexponentialmapping41-Finslermetric44-geodesie35,36--flow37339340SubjectIndexnonholonomicexponentialmapping(cont.
)-manifold,dimensionof48-Riemannianmanifold39--metric36-sphere36normalsubalgebra326one-parametersubgroup322orientabletoroidalsaddle283parallelotopetheorem43Pfaffiansystem14Plancherelmeasure249Poissonbracketll8,263-groupaction203Poisson-Liegroup198Poissonmanifoldll8-mappingll9-submanifold19-vector158polysystem(symmetric)44-,regular44prequantization229principalnilpotentelement235-seriesrepresentation239projectionassociatedwithadistribution32-method91Pukanszkycondition228quantization233quantumlinebundle228---,reduced228radialprojection92radical323rankofacovector274Rashevsky-Chowtheorem35R-bracket120realform326reducedsymplecticmanifold148reduction52,148regularelement324-point281-vector274Riemannproblern175,182,192"rigidbody"operator306r-matrix200root324-,imaginary138-,negative325-,positive138,325-,simple139,325rootdecompositionofanaffineLiealgebra138-system325-,affine138-vector324scatteringoperator249-transformation131-133sectionaloperator304-,compact308-,complexsemisimple307-,normal308semi-invariant3llsemisimpleelement327-operator327-orbit327separatrixdiagram290shiftofargument306singularelement324skewgradient263solutionoftheHamilton-Jacobiequation271sphericalcoordinates108-pendulum167-projection105S-representation312stabletrajectory287Steklovintegrablecase196strictlysymplecticaction278surgeryofLiouvilletori284symbolofaHamiltonian236symmetricspace327symplecticaction278-leaf119-mapping265-realization148-rankofasetoffunctions277-vector303symplectomorphism278theoremonthewavefront58-onadenseorbitfordistributions27-onadenseorbitforvectorfields30-ontheleadingterm45-onthelimitingformofpowersofadisk49Todalattice97,128,141-,nonabelian153-,nonperiodic128-,periodic141-,quantum238-,quaternionie154trouthers283Thurston'smanifold264Uhlenbeckintegrals162wavefront,nonholonomic41-operator249-packet245weightofarepresentation324-vector324Weylalcove97-basis326SubjectIndex-chamber97Whittakerfunction240-vector240Yang-Baxterequation123---,modified123341EncyclopaediaofMathematicalSeiencesEditor-in-Chief:R.
V.
GamkrelidzeDynamicalSystemsVolume1:D.
V.
Anosov,V.
I.
Arnol'd(Eds.
)DynamicalSystemsIOrdinaryDifferentialEquationsandSmoothDynamicalSystems1988.
IX,233pp.
25figs.
ISBN3-540-17000-6Volume2:Ya.
G.
Sinai(Ed.
)DynamicalSystemsIIErgodieTheorywithApplicationstoDynamicalSystemsandStatisticalMechanics1989.
IX,281pp.
25figs.
ISBN3-540-17001-4Volume3:V.
Amol'd(Ed.
)DynamicalSystems111MathematicalAspectsofClassicalandCelestialMechanics1988.
XIV,291pp.
81figs.
ISBN3-540-17002-2Volume4:V.
I.
Arnol'd,S.
P.
Novikov(Eds.
)DynamicalSystemsIVSymplecticGeometryanditsApplications1990.
VII,283pp.
62figs.
ISBN3-540-17003-0Volume5:V.
I.
Amol'd(Ed.
)DynamicalSystemsVBifurcationTheoryandCatastropheTheory1993.
Approx.
280pp.
130figs.
ISBN3-540-18173-3Volume6:V.
I.
Amol'd(Ed.
)DynamicalSystemsVISingularityTheoryIByV.
I.
Arnol'd,V.
V.
Goryunov,0.
V.
Lyashko,V.
A.
Vasil'evTranslatedfromtheRussianbyA.
Iacob1993.
V,245pp.
55figs.
ISBN3-540-50583-0Volume39:V.
I.
Arnol'd(Ed.
)DynamicalSystemsVIIISingularityTheoryII-Applications1993.
V,233pp.
134figs.
ISBN3-540-53376-1SpringerEncyclopaediaofMathematicalSeiencesEditor-in-Chief:R.
V.
GamkrelidzeSeveralComIexVariablesVolume7:A.
G.
Vitushkin(Ed.
)SeveralComplexVariablesIlntrodudiontoComplexAnalysis1989.
VII,248pp.
ISBN3·540-17004·9Volume8:G.
M.
Khenkin,A.
G.
Vitnshkin(Eds.
)SeveralComplexVariablesIIFundionTheoryinClassicalDomains.
ComplexPotentialTheory1993.
Approx.
260pp.
l9figs.
ISBN3·540·18175-XVolume9:G.
M.
Khenkin(Ed.
)SeveralComplexVariables111GeometrieFundionTheory1989.
VII,261pp.
ISBN3·540-17005·7Volume10:S.
G.
Gindikin,G.
M.
Khenkin(Eds.
)SeveralComplexVariablesIVAlgebraicAspectsofComplexAnalysis1990.
VII,251pp.
ISBN3·540·18174·1Volume54:G.
M.
Kenkin(Ed.
)SeveralComplexVariablesVConvolutionEquations.
ComplexGeometrywithApplicationstoPhysics1993.
VII,286pp.
ISBN3·540-54451·8Volume69:W.
Barth,R.
Narasimhan(Eds.
)SeveralComplexVariablesVIComplexManifolds1990.
IX,310pp.
4figs.
ISBN3·540·52788·5H.
Grauert,T.
Peternell,R.
Remmert(Eds.
)SeveralComplexVariablesVIISheaf·TheoreticalMethodsinComplexAnalysis1993.
Approx.
250pp.
ISBN3·540-56259·1AnalysisVolume13:R.
V.
Gamkrelidze(Ed.
)AnalysisIIntegralRepresentationsandAsymptoticMethods1989.
VII,238pp.
3figs.
ISBN3·540·17008·1Volume14:R.
V.
Gamkrelidze(Ed.
)AnalysisIIConvexAnalysisandApproximationTheory1990.
VII,255pp.
21figs.
ISBN3·540·18179·2Vo1ume26:S.
M.
Nikol'skij(Ed.
)Analysis111SpacesofDifferentiableFundions1991.
VII,221pp.
22figs.
ISBN3·540-51866-5Volume27:V.
G.
Maz'ya,S.
M.
Nikol'skij(Eds.
)AnalysisIVLinearandBoundaryIntegralEquations1991.
VII,233pp.
4figs.
ISBN3·540·51997·1Volume19:N.
K.
Nikol'skij(Ed.
)FunctionalAnalysisILinearFundionalAnalysis1992.
V,283pp.
ISBN3·540-50584·9Volume20:A.
L.
Onishchik(Ed.
)LieGroupsandLieAlgebrasIFoundationsofLieTheory.
LieGroupsofTransformations1993.
VII,235pp.
ISBN3·540·18697·2Springer
H.
185Adler,M.
117,126,147,174Akhiezer,N.
l.
177,182,187Alexandrov,A.
D.
5,8Anosov,D.
V.
288Appel,P.
5Arnol'd,V.
I.
8,160,266Baker,H.
F.
177,182,187Baxter,R.
198,219Belavin,A.
A.
126,190,197,219Benjamin,T.
B.
96Berezin,F.
A.
88,119,266Birman,M.
S.
250Bobenko,A.
l.
188,197Bogoyavlensky,0.
1.
114,133,147,174,318Bohr,N.
228Bolsinov,A.
V.
182,302,318,321Bore!
,A.
12Borovik,A.
E.
197Bott,R.
281Brailov,A.
V.
285,291,314,317,322Bruhat,F.
128,131,239Burmistrova,A.
B.
291Calogero,F.
95,96,100,102,114Caratheodory,C.
5,7,35,36Carnot,L.
7,35Casimir,H.
119,128,205,233,238Cartan,E.
5,7,14,15,20,22,39,98,109,128,138,155,161,164,171,174,234,277,324Cauchy,A.
37,106,109,112,247Chaplygin,S.
A.
5,285Cherednik,I.
V.
147,180,197Chernyakov,A.
G.
8,22,45Chevalley,C.
236,243Chow,W.
L.
4,7,35Chudnovsky,D.
V.
175Chudnovsky,G.
V.
175Clebsch,A.
163,174Cousin,J.
192Cristoffel,E.
B.
39,52,54DaoChongTkhi317Dirac,P.
A.
M.
5Drinfel'd,V.
G.
126,197,219Dubrovin,B.
A.
179Duflo,M.
233,238Dynkin,E.
B.
98,139Eliashberg,Ya.
M.
8Euler,L.
8,37,38,154,158,267Faddeev,L.
D.
8,198Filippov,A.
F.
37Finikov,S.
P.
36,39Flaschka,H.
144,133Floquet,G.
56Fomenko,A.
T.
160,182,268,275,282,284-298,304,306,308Fordy,A.
175,319Fourier,J.
H.
S.
176,249Franklin,G.
7Frenkel,I.
B.
126,147Frobenius,G.
4,12,316Fubini,G.
251Fuks,D.
B.
263Galois,E.
V.
246Garnier,R.
172Gel'fand,I.
M.
258Gibbs,J.
W.
5Gindikin,S.
G.
240,258Golod,P.
l.
197Goodman,R.
257Gorbatenko,E.
M.
6Goryachev,D.
N.
285Grassmann,H.
163Griffith,Ph.
4Gromov,M.
263,265Guillemin,V.
155,257,281Haar,A.
68,241Hall,M.
,Jr26Hamilton,W.
R.
88,270Harish-Chandra234,238,241,258Hausdorf,F.
48Heisenberg,W.
23,49Hertz,H.
4,5,7,9Hilbert,D.
269336AuthorIndexHlder,0.
5Hopf,H.
35,36Horak,M.
5Hrmander,L.
5lssaly6Its,A.
R.
179,188lvanov,N.
V.
8lwasawa,H.
130,235,239Jacobi,C.
J.
101,118,120,154,263,270Jacquet,H.
240,258Kac,V.
G.
98,146Kadomtsev,B.
B.
96Kagan,V.
F.
6,36Karasev,M.
V.
154Karpelevich,F.
240,258Kato,T.
250Kawaguchi,A.
36Kazhdan,D.
114,154Kharlamov,M.
P.
285Killing,W.
128,235,308Kirchhoff,P.
269Kirillov,A.
A.
88,119,229,266Klingenberg,W.
288Komarov,I.
V.
174Korteweg,D.
J.
5,269Kostant,B.
114,117,119,126,133,229,231,232Kowalewski,S.
V.
117,167,174,285Kozlov,V.
V.
9Krichever,I.
M.
113,179Lagrange,J.
Z.
16,37,38,117,166Landau,L.
D.
197Langlands,R.
242Laplace,P.
S.
238,249Laptev,G.
F.
22Laurent,P.
A.
99,133Lax,P.
87,100,104,114,117,121,155,250LeNgokT'euen316,317Lebesgue,H.
L.
251,269Legendre,A.
M.
156Leibniz,G.
W.
118,310Levi-Civita,T.
5Lie,S.
87,98,117,119,133,154,234,272,322Lifshitz,E.
M.
197Liouville,J.
91,271,272Liubich,Yu.
I.
8Lobachevsky,N.
l.
6,111Lumiste,Yu.
G.
8Macdonald,H.
M.
250Mackey,G.
W.
155Magri,F.
121,147,220Mamedov,G.
291Manakov,S.
V.
114,133,159,160,306Manin,Yu.
I.
202Marsden,J.
114,154Marshall,I.
175,319Matveev,S.
V.
291Matveev,V.
B.
179,188Maurer,L.
14Meshcheryakov,M.
V.
310Minkowski,H.
46Mishchenko,A.
S.
160,182,268,275,306,308Mittag-LeiDer,G.
188,190Moerbeke,P.
van126,147,174,180Moody,R.
98,146Moore,C.
L.
7Moser,J.
95,114,133,162,174Mumford,D.
126,180Narasimham,M.
265Neumann,C.
162Novikov,S.
P.
155,179,263Ol'shanetsky,M.
A.
114Ono,H.
96Oshemkov,A.
A.
300Perelomov,A.
M.
114,174Petrov,N.
N.
8Petviashvili,V.
l.
96Pfaff,F.
14Plancherel,M.
248,257Pogosyan,T.
I.
285Poincare,H.
315Poisson,S.
D.
88,118,119,148,158,198,231,263Polyakov,A.
M.
155Popov,V.
A.
265Pukanszky,L.
228Ragnisco,0.
174Ramanan,S.
265Rashevsky,P.
K.
4,7,35Ratiu,T.
155,174Rawnsley,J.
H.
155Reyman,A.
G.
126,147,155,160,174,180,182,188,197,257deRham,G.
228,273Riemann,B.
117,122,175,192Rinow,W.
35,36Roch,E.
179Routh,E.
5AuthorIndexSchiffmann,G.
240,254Schmeltzer,I.
155Schmidt,E.
269Schenberg,I.
7Schouten,J.
A.
6Schrdinger,E.
242,250Schwartz,L.
252Semenov-Tian-Shansky,M.
A.
126,147,155,160,174,180,182,188,197,219,257Shcherbakov,V.
N.
8Sinai,Ya.
G.
107Sintsov,D.
M.
6Sklyanin,E.
K.
197,198,201,214,219Sommerfeld,A.
228Souriau,J.
M.
119,155Stckel,P.
271Steklov,V.
A.
196Sternberg,S.
155,257,281Sussmann,H.
J.
36Sutherland,B.
95,100,102,107,114Synge,J.
l.
5,6Takens,F.
288Takhtajan,L.
A.
198Tischler,D.
265Toda,M.
97,102,111,126,141,153,226,234,238Trofimov,V.
V.
269,305,309-312,314,318Thurston,W.
264Uhlenbeck,K.
162Vagner,V.
V.
6,7,36Vassiliev,A.
M.
8Vergne,M.
311,318Vershik,A.
M.
45Veselov,A.
P.
197Vessio,E.
14Vinogradov,A.
M.
8Volterra,V.
5Voronets,P.
V.
5Voss,A.
5Vranceanu,G.
6,8deVries,G.
269Waldhausen,F.
291Wallach,N.
257Weierstrass,C.
87,96Weinstein,A.
114,119,154,220Weyl,H.
6,97,132,159,235,242,250,326Whitney,H.
25Whittaker,E.
238-242,257Wigner,E.
155Witt,E.
27Wojciechowski,S.
174,175,319Yang123Zieschang,H.
291337SubjectIndexAbeltransform185actionfunctional42adjointaction323-representation88,323admissiblecurveforadistribution10--forapolysystem44algorithm(a)314anharmonicoscillator172annihilatorofacovector274Baker-Akhiezerfunction183baseofarootsystem325basisofaregulardistribution17BaxterLiealgebra201bifurcationdiagram282Bohr-Zommerfeldcondition228Bore!
theorem12Bottfunction281Bruhatdecomposition128Carnot-Caratheodorymetric36Cartandecomposition156-matrix98,129,141-subalgebra128,324--,extended138Cartan'stheorem15Casimirfunction119-operator233classofafunctionalsystem277coadjointorbit88,119,265-representation88,119,323codistribution14coflagofaPfaffiansystem15collectivefunction280compactrealform326compactlyembeddedsubalgebra326completelyintegrablesystem271---,collective281---,inthenoncommutativesense275connectionasdistribution21-form21-overadistribution22contactstructure22coordinatesystemcompatiblewithabasis18Couzinproblern145,192Coxeterautomorphism98criticalpoint281-submanifold,nondegenerate281-value281cylinder283degreeofaconnection21-ofnonholonomicity14differentialsystem11diskintheReisenberggroup49dissipativesolidtorus283distribution10-,Cartan20-,completelynonholonomic14-,horizontal21-,integrable10-,involutive11-,ofmaximalgrowth25-,regular14double202dressingtransformation205dualpair148Dufloisomorphism233energyform247-space246equivalenceconjecture276Eulerequations156,267Euler-Lagrangeequations38Euler-Poissonequations158factorizationproblern122Filippov'sIemma37flagmanifold20-ofaconnection21-ofadifferentialsystem13-ofadistribution12flatconnection21Floquettheorem56Frobeniustheorem12functionalequationsforscatteringoperator250--forWhittakerfunctions240functionsininvolution263Garniersystem172gradingofanaffineLiealgebra139principal128,139GrassmannIibration10-manifold163growthdefectofadistribution28-vector14gyrostat166Hamilton-Jacobiproblern271Hamiltonian118,263-,reduced149-groupaction88,148,278-reduction147-subalgebra306-vectorfield118,268Harish-Chandrafunction241-homomorphism238heightofaroot128,139Heisenbergrepresentation189Hopf-Rinowtheorem36,37Hallfamily26Hall-Witttheorem27horosphericalCoordinates111-projection95ideal,differential15-,special15indexofaLiealgebra274inertiatensor155integral263-,Bott282-,complete270-,nonorientable287-,orientable287-form265-submanifold13invariant311Iwasawadecomposition130,235jetofadistribution12-ofavectorfield11Kac-Moodyalgebra98,146kinematicsofarigidbody155Kirillovbracket88,119,266-form88,266Korteweg-deVriesequation269Kawalewskitop167Lagrangemultiplier37-top166Lagrangiansubalgebra227-submanifold270SubjectIndexLanglandsdecomposition242Laxequation87,121Iemmaonquasitriangularform17lengthfunctional36Liealgebra322-,affine133,137-,compact326-,double202-,Frobenius316-,graded126-,nilpotent323-,orthogonalsymmetric327-,selfadjoint316-,semisimple323-,simple323-,solvable323-,withPoincareduality315Liebialgebra200--,factorizable201Liegroup322Lie-Poissonbracket119Lie'stheorem272Iift278linearbundle,regular178Liouville'stheorem272--,noncommutative275loopalgebra133--,twisted133magneticbundle150-form151Manintriple202Maurer-Cartanformula15Mittag-Leffiertheorem189mixedbundle("centaure")16,37momentmap89,148,279monodromymapping57-submanifold62Morsepotential131motionofarigidbodyinfluid,Clebschcase163-------,Steklovcase196multidimensionalrigidbody155-172---,equationsofmotion156,268---,inaquadraticpotential162Neumannsystem162--,inmonopalefield162nilpotentelement327-operator327nonholonomicexponentialmapping41-Finslermetric44-geodesie35,36--flow37339340SubjectIndexnonholonomicexponentialmapping(cont.
)-manifold,dimensionof48-Riemannianmanifold39--metric36-sphere36normalsubalgebra326one-parametersubgroup322orientabletoroidalsaddle283parallelotopetheorem43Pfaffiansystem14Plancherelmeasure249Poissonbracketll8,263-groupaction203Poisson-Liegroup198Poissonmanifoldll8-mappingll9-submanifold19-vector158polysystem(symmetric)44-,regular44prequantization229principalnilpotentelement235-seriesrepresentation239projectionassociatedwithadistribution32-method91Pukanszkycondition228quantization233quantumlinebundle228---,reduced228radialprojection92radical323rankofacovector274Rashevsky-Chowtheorem35R-bracket120realform326reducedsymplecticmanifold148reduction52,148regularelement324-point281-vector274Riemannproblern175,182,192"rigidbody"operator306r-matrix200root324-,imaginary138-,negative325-,positive138,325-,simple139,325rootdecompositionofanaffineLiealgebra138-system325-,affine138-vector324scatteringoperator249-transformation131-133sectionaloperator304-,compact308-,complexsemisimple307-,normal308semi-invariant3llsemisimpleelement327-operator327-orbit327separatrixdiagram290shiftofargument306singularelement324skewgradient263solutionoftheHamilton-Jacobiequation271sphericalcoordinates108-pendulum167-projection105S-representation312stabletrajectory287Steklovintegrablecase196strictlysymplecticaction278surgeryofLiouvilletori284symbolofaHamiltonian236symmetricspace327symplecticaction278-leaf119-mapping265-realization148-rankofasetoffunctions277-vector303symplectomorphism278theoremonthewavefront58-onadenseorbitfordistributions27-onadenseorbitforvectorfields30-ontheleadingterm45-onthelimitingformofpowersofadisk49Todalattice97,128,141-,nonabelian153-,nonperiodic128-,periodic141-,quantum238-,quaternionie154trouthers283Thurston'smanifold264Uhlenbeckintegrals162wavefront,nonholonomic41-operator249-packet245weightofarepresentation324-vector324Weylalcove97-basis326SubjectIndex-chamber97Whittakerfunction240-vector240Yang-Baxterequation123---,modified123341EncyclopaediaofMathematicalSeiencesEditor-in-Chief:R.
V.
GamkrelidzeDynamicalSystemsVolume1:D.
V.
Anosov,V.
I.
Arnol'd(Eds.
)DynamicalSystemsIOrdinaryDifferentialEquationsandSmoothDynamicalSystems1988.
IX,233pp.
25figs.
ISBN3-540-17000-6Volume2:Ya.
G.
Sinai(Ed.
)DynamicalSystemsIIErgodieTheorywithApplicationstoDynamicalSystemsandStatisticalMechanics1989.
IX,281pp.
25figs.
ISBN3-540-17001-4Volume3:V.
Amol'd(Ed.
)DynamicalSystems111MathematicalAspectsofClassicalandCelestialMechanics1988.
XIV,291pp.
81figs.
ISBN3-540-17002-2Volume4:V.
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Arnol'd,S.
P.
Novikov(Eds.
)DynamicalSystemsIVSymplecticGeometryanditsApplications1990.
VII,283pp.
62figs.
ISBN3-540-17003-0Volume5:V.
I.
Amol'd(Ed.
)DynamicalSystemsVBifurcationTheoryandCatastropheTheory1993.
Approx.
280pp.
130figs.
ISBN3-540-18173-3Volume6:V.
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Amol'd(Ed.
)DynamicalSystemsVISingularityTheoryIByV.
I.
Arnol'd,V.
V.
Goryunov,0.
V.
Lyashko,V.
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Vasil'evTranslatedfromtheRussianbyA.
Iacob1993.
V,245pp.
55figs.
ISBN3-540-50583-0Volume39:V.
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Arnol'd(Ed.
)DynamicalSystemsVIIISingularityTheoryII-Applications1993.
V,233pp.
134figs.
ISBN3-540-53376-1SpringerEncyclopaediaofMathematicalSeiencesEditor-in-Chief:R.
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GamkrelidzeSeveralComIexVariablesVolume7:A.
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Vitushkin(Ed.
)SeveralComplexVariablesIlntrodudiontoComplexAnalysis1989.
VII,248pp.
ISBN3·540-17004·9Volume8:G.
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Khenkin,A.
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Vitnshkin(Eds.
)SeveralComplexVariablesIIFundionTheoryinClassicalDomains.
ComplexPotentialTheory1993.
Approx.
260pp.
l9figs.
ISBN3·540·18175-XVolume9:G.
M.
Khenkin(Ed.
)SeveralComplexVariables111GeometrieFundionTheory1989.
VII,261pp.
ISBN3·540-17005·7Volume10:S.
G.
Gindikin,G.
M.
Khenkin(Eds.
)SeveralComplexVariablesIVAlgebraicAspectsofComplexAnalysis1990.
VII,251pp.
ISBN3·540·18174·1Volume54:G.
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Kenkin(Ed.
)SeveralComplexVariablesVConvolutionEquations.
ComplexGeometrywithApplicationstoPhysics1993.
VII,286pp.
ISBN3·540-54451·8Volume69:W.
Barth,R.
Narasimhan(Eds.
)SeveralComplexVariablesVIComplexManifolds1990.
IX,310pp.
4figs.
ISBN3·540·52788·5H.
Grauert,T.
Peternell,R.
Remmert(Eds.
)SeveralComplexVariablesVIISheaf·TheoreticalMethodsinComplexAnalysis1993.
Approx.
250pp.
ISBN3·540-56259·1AnalysisVolume13:R.
V.
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)AnalysisIIntegralRepresentationsandAsymptoticMethods1989.
VII,238pp.
3figs.
ISBN3·540·17008·1Volume14:R.
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Gamkrelidze(Ed.
)AnalysisIIConvexAnalysisandApproximationTheory1990.
VII,255pp.
21figs.
ISBN3·540·18179·2Vo1ume26:S.
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Nikol'skij(Ed.
)Analysis111SpacesofDifferentiableFundions1991.
VII,221pp.
22figs.
ISBN3·540-51866-5Volume27:V.
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Nikol'skij(Eds.
)AnalysisIVLinearandBoundaryIntegralEquations1991.
VII,233pp.
4figs.
ISBN3·540·51997·1Volume19:N.
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Nikol'skij(Ed.
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V,283pp.
ISBN3·540-50584·9Volume20:A.
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LieGroupsofTransformations1993.
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ISBN3·540·18697·2Springer
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