Symplectic twist maps : global variational techniques / Christophe Gole.

Format:

Book

Author/Creator:

Golé, Christophe.

Series:

Advanced series in nonlinear dynamics ; v. 18.

Advanced series in nonlinear dynamics ; v. 18

Language:

English

Subjects (All):

Twist mappings (Mathematics).

Mappings (Mathematics).

Physical Description:

1 online resource (324 p.)

Edition:

1st ed.

Place of Publication:

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

Language Note:

English

Summary:

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

Contents:

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

Notes:

Description based upon print version of record.

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

ISBN:

9786611956394

9781281956392

1281956392

9789812810762

9812810765

OCLC:

881611083