Table Of ContentHamiltonian Systems with
Three or More Degrees of Freedom
NATO ASI Series
AdvancedScienceInstituteSeries
ASeriespresentingtheresultsofactivitiessponsoredbytheNATOScienceCommittee,
whichaimsatthedisseminationofadvancedscientificandtechnologicalknowledge,
withaviewtostrengtheninglinksbetweenscientificcommunities.
TheSeriesispublishedbyaninternationalboardofpublishersinconjunctionwiththeNATO
ScientificAffairsDivision
A. LifeSciences PlenumPublishingCorporation
B. Physics LondonandNewYork
C. MathematicalandPhysicalSciences KluwerAcademicPublishers
D. BehaviouralandSocialSciences Dordrecht,BostonandLondon
E. AppliedSciences
F. ComputerandSystemsSciences Springer-Verlag
G. EcologicalSciences Berlin,Heidelberg,NewYork,London,
H. CellBiology ParisandTokyo
I. GlobalEnvironmentChange
PARTNERSHIPSUB-SERIES
1. DisarmamentTechnologies KluwerAcademicPublishers
2. Environment Springer-VerlagIKluwerAcademicPublishers
3. HighTechnology KluwerAcademicPublishers
4. ScienceandTechnologyPolicy KluwerAcademicPublishers
5. ComputerNetworking KluwerAcademicPublishers
ThePartnerschipSub-SeriesincorporatesactivitiesundertakenincollaborationwithNATO's
CooperationPartners, thecountriesoftheCISandCentralandEasternEurope, inPriorityAreasof
concerntothosecountries.
NATO-PCO-DATABASE
The electronic index to the NATOASI Series provides full bibliographical references (with keywords
and/orabstracts)toabout50,000contributionsfrom internationalscientistspublishedinallsectionsof
theNATOASISeries.AccesstotheNATO-PCO-DATA-BASEispossibleviaaCD-ROM"NATOScience
and Technology Disk" with user-friendly retrieval software in English, French, and German (©WTV
GmbHandDATAWARETechnologies,Inc. 1989).TheCD-ROMcontainstheAGARDAerospaceData
base.
TheCD-ROMcanbeorderedthroughanymemberoftheBoardofPublishersorthroughNATO-PCO,
Overijse,Belgium.
SeriesC: MathematicalandPhysicalSciences- Vol.533
Hamiltonian Systems with
Three or More Degrees of Freedom
edited by
Carles Sim6
Universitat de Barcelona,
Barcelona, Spain
....
"
Springer-Science+Business Media, B.V.
Proceedings of the NATO Advanced Study Institute on
Hamiltonian Systems with Three or More Oegrees of Freedom
S'Agar6, Spain
June 19-30, 1995
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-5968-8 ISBN 978-94-011-4873-9 (eBook)
DOI 10.1007/978-94-011-4673-9
Printed on acid-free paper
AII Rights Reserved
© 1999 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint of the hardcover 1s t edition 1999
No part of the material protected by this copyright notice may be reproduced ar utilized in
any form or by any means, electronic or mechanical, including phatocopying, recording or
by any information storage and retrieval system, without written permission from the
copyright owner.
Table of contents
LECTURES
S. Angenent 3
INFLECTION POINTS, EXTATIC POINTS AND CURVE
SHORTENING
V.I. Arnold 11
TOPOLOGICALLY NECESSARY SINGULARITIES ON MOVING
WAVEFRONTS AND CAUSTICS
S.V. Bolotin 13
HETEROCLINIC CHAINS OF SKEW PRODUCT HAMILTONIAN
SYSTEMS
G. Contopoulos, N. Voglis, C. Efthymiopoulos 26
ORDER AND CHAOS IN 3-D SYSTEMS
A. Delshams, R. Ramirez-Ros, T.M. Seara 39
SPLITTING OF SEPARATRICES IN HAMILTONIAN SYSTEMS
AND SYMPLECTIC MAPS
L.R. Eliasson 55
ON THE DISCRETE ONE-DIMENSIONAL QUASI-PERIODIC
SCHRODINGER EQUATION AND OTHER SMOOTH
QUASI-PERIODIC SKEW PRODUCTS
G. Gallavotti 62
LINDSTEDT SERIES AND KOLMOGOROV THEOREM
A. Giorgilli, U. Locatelli 72
A CLASSICAL SELF-CONTAINED PROOF OF KOLMOGOROV'S
THEOREM ON INVARIANT TORI
vi
P. Boyland, C. Gole 90
DYNAMICAL STABILITY IN LAGRANGIAN SYSTEMS
J. Henrard 115
THE ORIGIN OF CHAOTIC BEHAVIOUR IN THE KIRKWOOD
GAPS
M. Herman 126
EXAMPLES OF COMPACT HYPERSURFACES IN R2P, 2P ~ 6,
WITH NO PERIODIC ORBITS
V.V. Kozlov 127
HAMILTONIAN SYSTEMS WITH THREE DEGREES OF
FREEDOM AND HYDRODYNAMICS
J. Laskar 134
INTRODUCTION TO FREQUENCY MAP ANALYSIS
A. Jorba, R. de la Llave, M. Zou 151
LINDSTEDT SERIES FOR LOWER DIMENSIONAL TORI
P. Lochak 168
ARNOLD DIFFUSION; A COMPENDIUM OF REMARKS
AND QUESTIONS
J. Moser 184
OLD AND NEW APPLICATIONS OF KAM THEORY
A. Neishtadt 193
ON ADIABATIC INVARIANCE IN TWO-FREQUENCY SYSTEMS
J. Seimenis 213
THE METHOD OF RATIONAL APPROXIMATIONS:
THEORY AND APPLICATIONS
C. Sim6 223
DYNAMICAL SYSTEMS METHODS FOR SPACE MISSIONS
ON A VICINITY OF COLLINEAR LIBRATION POINTS
vii
Va. G. Sinai 242
A MECHANISM OF ERGODICITY IN STANDARD--LIKE MAPS
D.V. Treschev 244
CONTINUOUS AVERAGING IN HAMILTONIAN SYSTEMS
S. Wiggins 254
PHASE SPACE GEOMETRY AND DYNAMICS ASSOCIATED
WITH THE 1:2:2 RESONANCE
H. Yoshida 270
FROM SINGULAR POINT ANALYSIS TO RIGOROUS RESULTS
ON INTEGRABILITY: A DREAM OF S. KOWALEVSKAYA
CONTRIBUTIONS
S. Abenda 285
TIME SINGULARITIES FOR POLYNOMIAL HAMILTONIANS
WITH ANALYTIC TIME DEPENDENCE
M. Antoni, C. Sandoz, Y. Elskens 290
NUMERICAL STUDY OF TURBULENCE IN N-BODY HAMILTON
IAN SYSTEMS WITH LONG RANGE FORCE I. RELAXATION
K.M. Atkins, M. Hutson 295
PHASE SPACE STRUCTURES IN 3 AND 4 DEGREES OF
FREEDOM: APPLICATION TO CHEMICAL REACTIONS
A. Bazzani, F. Brini 300
MODULATED DIFFUSION FOR SYMPLECTIC MAPS
G. Benettin 305
ON THE JEANS-LANDAU-TELLER APPROXIMATION FOR
ADIABATIC INVARIANTS
viii
R.M. Benito, F. Borondo 310
PERIODIC ORBITS AND QUANTUM MECHANICS OF
MOLECULAR HAMILTONIAN SYSTEMS
F. Borondo, J. Bowers, R. Guantes, Ch. Jaffe, S. Miret-Artes 314
CHAOS IN ATOM-SURFACE COLLISIONS
T. Bountis, L. Drossos 318
ON THE NON-INTEGRABILITY OF THE MIXMASTER
UNIVERSE MODEL
S.A. Dovbysh 324
BRANCHING OF SOLUTIONS AS OBSTRUCTION TO THE
EXISTENCE OF A MEROMORPHIC INTEGRAL IN MANY
DIMENSIONAL SYSTEMS
H.R. Dullin 330
THE ENERGY SURFACES OF THE KOVALEVSKAYA-TOP
H.S. Dumas 335
FILLING RATES FOR LINEAR FLOW ON THE TORUS:
RECENT PROGRESS AND APPLICATIONS
N. Voglis, C. Efthymiopoulos, G. Contopoulos 340
INVARIANT SPECTRA OF ORBITS IN MULTIDIMENSIONAL
SYMPLECTIC MAPS
L. Chierchia, C. Falcolini 345
ON THE CONVERGENCE OF FORMAL SERIES CONTAINING
SMALL DIVISORS
Y.N. Fedorov 350
SYSTEMS WITH AN INVARIANT MEASURE ON LIE GROUPS
S. Ferraz-Mello 357
STOCHASTICITY OF THE 2/1 ASTEROIDAL RESONANCE:
A SYMPLECTIC MAPPING APPROACH
ix
S. Ferrer, M. Lara, J. Palacian, P. Yanguas 362
ON PERTURBED OSCILLATORS IN 1-1 - 1RESONANCE: CRIT
ICAL INCLINATION IN THE 3D HENON-HEILES POTENTIAL
A. Delshams, Y. Gelfreich, A. Jorba, M.T. Seara 367
SPLITTING OF SEPARATRICES FOR (FAST) QUASIPERIODIC
FORCING
G. Gentile, Y. Mastropietro 372
A POSSIBLE MECHANISM FOR THE KAM TORI BREAKDOWN
c.
Grotta Ragazzo 377
ON THE DYNAMICS NEAR RESONANT EQUILIBRIA
A. Delshams, P. Gutierrez 386
EXPONENTIALLY SMALL ESTIMATES FOR KAM THEOREM
NEAR AN ELLIPTIC EQUILIBRIUM POINT
G. Haller 391
FAST DIFFUSION AND UNIVERSALITY NEAR INTERSECTING
RESONANCES
H. Han13mann 398
QUASI-PERIODIC MOTION OF A RIGID BODY UNDER WEAK
FORCES
A.Haro 403
CENTERAND CENTER-(UN)STABLE MANIFOLDS OF ELLIPTIC
HYPERBOLIC FIXED POINTS OF 4D-SYMPLECTIC MAPS. AN
EXAMPLE: THE FROESCHLE MAP
P.G. Hjorth 408
A MANY-PARTICLE ADIABATIC INVARIANT
S. Ichtiaroglou, E. Meletlidou 413
THE NON-INTEGRABILITY OF PERTURBED HAMILTONIANS
OF N DEGREES OF FREEDOM AND THE CONTINUATION OF
PERIODIC ORBITS
x
M.Irigoyen 418
STRUCTURE OF THE 5-DIMENSIONAL MANIFOLD OF
CONSTANT ENERGY IN THE h-PROBLEM
J.A. Steckel, Ch. Jaffe 422
THE BIFURCATIONS OF THE LANGMUIR ORBIT IN THE
TWO-ELECTRON ATOM
H.R. Jauslin, M. Govin, M. Cibils 426
DOMAINS OF CONVERGENCE OF KAM TYPE ITERATIONS
FOR EIGENVALUE PROBLEMS
A.. Jorba, J. Masdemont 430
NONLINEAR DYNAMICS IN AN EXTENDED NEIGHBOURHOOD
OF THE TRANSLUNAR EQUILIBRIUM POINT
S. Keshavamurthy, G.S. Ezra 435
ANALYSIS OF QUANTUM EIGENSTATES IN A 3-MODE SYSTEM
T. Konishi 440
DETECTION OF STABLE MANIFOLDS IN HIGH DIMENSIONAL
PHASE SPACE
T. Konishi 444
ORDERED MOTION IN HAMILTONIAN SYSTEMS WITH MANY
DEGREES OF FREEDOM
I.Yu. Kostyukov, G.M. F'raiman 449
SOME RELATIONS FROM HAMILTONIAN MECHANICS AND
THEIR APPLICATIONS TO PLASMA PHYSICS
A. Delshams, J.T. Lazaro 453
EFFECTIVE STABILITY IN REVERSIBLE SYSTEMS
O.Yu. Koltsova, L.M. Lerman 458
NEW CRITERION OF NONINTEGRABILITY FOR AN
N-DEGREES-OF-FREEDOM HAMILTONIAN SYSTEM
