Hamiltonian dynamical systems: a reprint selection PDF
Preview Hamiltonian dynamical systems: a reprint selection
Hamiltonian Dynamical Systems Hamiltonian Dynamical Systems areprint selection compiled and introduced by R SMacKay , MathematicsInstitute UniversityofWarwick and J D Meiss InstituteforFusion Studies University ofTexas, Austin Publishedin 1987 by PublishedinGreatBritainby Taylor& FrancisGroup Taylor& FrancisGroup 270MadisonAvenue 2ParkSquare NewYork, NY 10016 MiltonPark, Abingdon Oxon0X144RN © 1987 byTaylor& FrancisGroup,LLC Noclaimto originalU.S. Governmentworks PrintedintheUnitedStates ofAmericaonacid-freepaper 10 9 8 7 6 5 4 3 2 InternationalStandardBookNumber-10:0-85274-205-3 (Hardcover) InternationalStandardBookNumber-13:978-0-85274-205-1 (Hardcover) ConsultantEditor:ProfessorRFStreater,UniversityofLondon This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted withpermission, and sources areindicated. A widevariety ofreferences are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility forthevalidityofall materialsorfortheconsequencesoftheiruse. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording,orinany information storageorretrievalsystem, withoutwrittenpermissionfromthepublishers. Trademark Notice:Productorcorporatenamesmaybetrademarksorregisteredtrademarks, andareusedonly foridentificationandexplanationwithoutintenttoinfringe. Library ofCongressCataloging-in-Publication Data Catalogrecordisavailable fromtheLibraryofCongress 1 i l l | mj| ll M l # j| VisittheTaylor&Francis Website at I I I I \aJr 1 I I I http://www.taylorandfrancis.com Taylor &FrancisGroup isthe Academic Divisionof Informa pic. Contents Preface Part 1:Introductory articles SurveyofHamiltoniandynamics R SMacKay andJDMeiss Is the SolarSystemstable? JKMoser Math. Intelligencer1 65-71 (1978) Regular andirregularmotion M VBerry Topics inNonlinearDynamics (ed SJorna), Am. Inst. Phys. Conf. Proc. 46 16-120 (1978) The mechanisms ofstochasticityin classical dynamical systems A S Wightman Perspectives in StatisticalPhysics (ed HJRaveche) pp 343-63 (1981) Part 2:Equilibria andperiodic orbits Lectures onHamiltoniansystems JKMoser Mem. Am. Math. Soc. 811-60 (1968) StabilityofequilibriaofHamiltoniansystems R S MacKay NonlinearPhenomena and Chaos (edSarben Sarkar) pp 254-70 (1986) Onthe periodicmotionsofdynamical systems GDBirkhoff Acta. Math. 50359-79 (1927) Linear stabilityofperiodicorbits in Lagrangiansystems RSMacKayandJDMeiss Phys. Lett. 98A92-4 (1983) vi Contents Generic bifurcationofperiodicpoints 178 KRMeyer Trans. Am. Math. Soc. 14995-107 (1970) Universal behaviourinfamiliesofarea-preserving maps 191 JMGreene, R S MacKay, FVivaldiandMJFeigenbaum Physica 3D468-86 (1981) Quasi-ellipticperiodic pointsin conservative dynamical systems 210 S ENewhouse Am. J.Math. 99 1061-87 (1977) Part 3:Quasiperiodicorbits Geodesics on a two-dimensional Riemannianmanifoldwith periodiccoefficients 239 GA Hedlund Ann. Math. 33 719-39 (1932) Small denominators andproblems ofstabilityofmotionin classicaland celestialmechanics 260 VIArnol’d Russ. Math. Surveys 18:685-191 (1963) Variational principles for invarianttori and cantori 367 IC Percival NonlinearDynamics and theBeam-Beam Interaction (ed MMonth andJCHerrera),Am. Inst. Phys. Conf. Proc. 57 302-10 (1979) Periodicand quasi-periodic orbits for twistmaps 376 A Katok Dynamical Systems and Chaos (ed LGarrido), SpringerLect. NotesPhys. 179 47-65 (1983) Non-existence ofinvariantcircles 395 JN Mather Erg. Theor. Dyn. Sys. 4 301-9 (1984) Part4:Breakup ofinvarianttori Resonanceprocessesinmagnetictraps 407 BVChirikov J. Nucl. EnergyC1253-60 (1960) Destructionofmagnetic surfacesby magneticfieldirregularities 415 MN Rosenbluth, RZSagdeev, JBTaylorandGM Zaslavski Nucl. Fusion 6297-300 (1966) Contents vii A methodfor determining astochastictransition 419 JM Greene J. Math.Phys. 20 1183- 201 (1979) Fractal diagramsfor Hamiltonianstochasticity 438 GSchmidtandJ Bialek Physica 5D397-404 (1982) Large-scale stochasticityinHamiltoniansystems 446 DFEscande Physica Scripta T2/1 126-41 (1982) A renormalisation approachto invariantcirclesinarea- preservingmaps 462 R S MacKay Physica 7D283-300 (1983) Part 5:Chaotic behaviour Roughness ofgeodesic flowsoncompactRiemannianmanifolds ofnegative curvature 483 DVAnosov Sov. Math.-Dokl. 31068-70 (1962) Ergodic propertiesofgeodesicflowsonclosedRiemannian manifoldsofnegativecurvature 486 DVAnosov Sov. Math.-Dokl. 4 1153-6 (1963) Markovpartitionsand C-diffeomorphisms 490 YaG Sinai Funct. Anal. Appl. 261-82 (1968) Ljapunov characteristicexponents and ergodicpropertiesof smoothdynamical systemswith an invariantmeasure 512 JaBPesin Sov. Math.-Dokl. 17 196-9 (1976) Ergodicityoflinkedtwistmaps 516 RBurtonandRWEaston SpringerLed. NotesMath. 819 35-49 (1980) Principlesforthedesignofbilliardswithnonvanishing Lyapunov exponents 531 MWojtkowski Commun. Math. Phys. 105 391-414 (1986) viii Contents Shiftautomorphismsinthe Henonmapping 555 RDevaneyandZ Nitecki Commun. Math. Phys. 67 137-46 (1979) Part 6:Mixed systems Amodel problemwiththe coexistenceofstochasticand integrablebehaviour 569 M Wojtkowski Commun. Math. Phys. 80 453-64 (1981) Fat fractals onthe energysurface 581 DKUmberger andJD Farmer Phys. Rev. Lett. 55661-4 (1985) Long-timecorrelationsinthe stochastic regime 585 CFF Karney Physica 8D360-80 (1983) Transport inHamiltoniansystems 606 R S MacKay, JDMeissandIC Percival Physica 13D55-81 (1984) Instabilityofdynamical systemswithseveral degreesoffreedom 633 VIArnol’d Sov. Math.- Dokl. 5581-5 (1964) Behavior ofHamiltoniansystemscloseto integrable 638 N N Nekhoroshev Funct. Anal. Appl. 5338-9 (1971) Melnikov’s method andArnold diffusionfor perturbations ofintegrableHamiltonian systems 640 PJHolmesandJEMarsden J.Math. Phys. 23 669-75 (1982) Arnold diffusion, ergodicity andintermittencyin acoupled standardmapping 647 KKanekoandRJBagley Phys. Lett. 110A 435-40 (1985) Part 7:Applications Nature ofthe Kirkwood gapsinthe asteroidbelt 655 SF Dermottand C DMurray Nature 301 201-5 (1983) Contents ix The chaotic rotationofHyperion 660 JWisdom, SJ Peale and FMignard Icarus 58137-52 (1984) A methodfor mapping a toroidal magneticfieldby storage of phasestabilizedelectrons 676 RMSinclair, JC Hoseaand GVSheffield Rev. Sci. Instrum. 41 1552-9 (1970) Electron heattransport in a tokamakwithdestroyed magnetic surfaces 684 A B Rechesterand M N Rosenbluth Phys. Rev. Lett. 40 38-41 (1978) Eliminationofstochasticityinstellerators 688 JDHansonandJRCary Phys. Fluids 27 767-9 (1984) The dynamicsofthebeam-beaminteraction 691 A Gerasimov, F M Izrailev, J LTennyson andA BTemnykh NonlinearDynamicsAspects ofParticle Accelerators (ed JMJowett, M Monthand S Turner), SpringerLed. NotesPhys. 247 154-75 (1986) Intramoleculardynamics andnonlinearmechanicsofmodel OCS 710 DCarterand PBrumer J. Chem. Phys. 774208-21 (1982) Stirring by chaoticadvection 725 HAref J. FluidMech. 143 1-21 (1984) The twistmap,theextended Frenkel-Kontorovamodel and the devil’sstaircase 746 S Aubry Physica 7D240-58 (1983) Part 8:Bibliography References 767
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