05085nam 2200661Ia 450 991078227410332120230607222141.01-281-95639-29786611956394981-281-076-5(CKB)1000000000538133(EBL)1679288(OCoLC)881611083(SSID)ssj0000254705(PQKBManifestationID)11207024(PQKBTitleCode)TC0000254705(PQKBWorkID)10209245(PQKB)10155834(MiAaPQ)EBC1679288(WSP)00001349(Au-PeEL)EBL1679288(CaPaEBR)ebr10255566(CaONFJC)MIL195639(EXLCZ)99100000000053813320020701d2001 uy 0engur|n|---|||||txtccrSymplectic twist maps[electronic resource] global variational techniques /Christophe GoléSingapore ;River Edge, NJ World Scientificc20011 online resource (324 p.)Advanced series in nonlinear dynamics ;v. 18Description based upon print version of record.981-02-0589-9 Includes bibliographical references (p. [293]-301) and index.Content ; Foreword ; 0 Introduction ; 1 Fall from Paradise ; 2 Billiards and Broken Geodesies ; 3 An Ancestor of Symplectic Topology ; 1 Twist Maps of the Annulus ; 4 Monotone Twist Maps of the Annulus ; 5 Generating Functions and Variational Setting ; 6 Examples7 The Poincare-Birkhoff Theorem 2 The Aubry-Mather Theorem ; 8 Introduction ; 9 Cyclically Ordered Sequences And Orbits ; 10 Minimizing Orbits ; 11 CO Orbits Of All Rotation Numbers ; 12 Aubry-Mather Sets ; 3 Ghost Circles ; 13 Appendix: Cyclically Ordered Sequences and Circle Maps14 Gradient Flow of the Action 15 The Gradient Flow and the Aubry-Mather Theorem ; 16 Ghost Circles ; 17 Construction of Ghost Circles ; 18 Construction of Disjoint Ghost Circles ; 19 Proof of Lemma 18.5 ; 20 Proof of Theorem 18.1 ; 21* Remarks and Applications22 Proofs of Monotonicity and of the Sturmian Lemma 4 Symplectic Twist Maps ; 23 Symplectic Twist Maps of Tn x Rn ; 24 Examples ; 25 More on Generating Functions ; 26 Symplectic Twist Maps on General Cotangent Bundles of Compact Manifolds5 Periodic Orbits for Symplectic Twist Maps of T*Tn 27 Presentation Of The Results ; 28 Finite Dimensional Variational Setting ; 29 Second Variation and Nondegenerate Periodic Orbits ; 30 The Coercive Case ; 31 Asymptotically Linear Systems ; 32 Ghost Tori33 Hyperbolicity Vs. Action Minimizers This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse Theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors. <br><i>Contents: </i><ul><li>Twist Maps of the Annulus</li><li>The Aubry-Mather Theorem</li><li>Ghost Circles</li><li>Symplectic TwAdvanced series in nonlinear dynamics ;v. 18.Twist mappings (Mathematics)Mappings (Mathematics)Twist mappings (Mathematics)Mappings (Mathematics)514.74Golé Christophe1495489MiAaPQMiAaPQMiAaPQBOOK9910782274103321Symplectic twist maps3719577UNINA