1.

Record Nr.

UNINA9910782274103321

Autore

Golé Christophe

Titolo

Symplectic twist maps [[electronic resource] ] : global variational techniques / / Christophe Golé

Pubbl/distr/stampa

Singapore ; ; River Edge, NJ, : World Scientific, c2001

ISBN

1-281-95639-2

9786611956394

981-281-076-5

Descrizione fisica

1 online resource (324 p.)

Collana

Advanced series in nonlinear dynamics ; ; v. 18

Disciplina

514.74

Soggetti

Twist mappings (Mathematics)

Mappings (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (p. [293]-301) and index.

Nota di contenuto

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 Examples

7 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 Maps

14 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 Applications

22 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 Manifolds

5 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 Tori

33 Hyperbolicity Vs. Action Minimizers

Sommario/riassunto

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 Tw