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Symplectic twist maps : global variational techniques / / Christophe Gole



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Autore: Gole Christophe Visualizza persona
Titolo: Symplectic twist maps : global variational techniques / / Christophe Gole Visualizza cluster
Pubblicazione: Singapore ; ; River Edge, NJ, : World Scientific, c2001
Edizione: 1st ed.
Descrizione fisica: 1 online resource (324 p.)
Disciplina: 514.74
Soggetto topico: Twist mappings (Mathematics)
Mappings (Mathematics)
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
Titolo autorizzato: Symplectic twist maps  Visualizza cluster
ISBN: 1-281-95639-2
9786611956394
981-281-076-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910826332603321
Lo trovi qui: Univ. Federico II
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Serie: Advanced series in nonlinear dynamics ; ; v. 18.