Author 
Golé, Christophe.

Series 
Advanced series in nonlinear dynamics ; v. 18 

Advanced series in nonlinear dynamics ;
v. 18.

Subject 
Twist mappings (Mathematics)

Description 
1 online resource (xviii, 301 pages) : illustrations. 

polychrome rdacc 
Bibliography Note 
Includes bibliographical references (pages 293301) and index. 
Contents 
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 PoincareBirkhoff theorem  2. The AubryMather theorem. 8. Introduction. 9. Cyclically ordered sequences and orbits. 10. Minimizing orbits. 11. CO orbits of all rotation numbers. 12. AubryMather sets  3. Ghost circles. 14. Gradient flow of the action. 15. The gradient flow and the AubryMather 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 T[symbol] x IR[symbol]. 24. Examples. 25. More on generating functions. 2.6. Symplectic twist maps on general cotangent bundles of compact manifolds  5. Periodic orbits for symplectic twist maps of T[symbol] x IR[symbol]. 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  6. Invariant manifolds. 34. The theory of KolmogorovArnoldMoser. 35. Properties of invariant tori. 36. (Un)stable manifolds and heteroclinic orbits. 37. Instability, transport and diffusion  7. Hamiltonian systems vs. twist maps. 38. Case study: The geodesic flow. 39. Decomposition of Hamiltonian maps into twist maps. 40. Return maps in Hamiltonian systems. 41. Suspension of symplectic twist maps by Hamiltonian flows  8. Periodic orbits for Hamiltonian systems. 42. Periodic orbits in the cotangent of the ntorus. 43. Periodic orbits in general cotangent spaces. 44. Linking of spheres  9. Generalizations of the AubryMather theorem. 45. Theory for functions on lattices and PDE's. 46. Monotone recurrence relationst. 47. Antiintegrable limit. 48. Mather's theory of minimal measures. 49. The case of hyperbolic manifolds. 50. Concluding remarks  10. Generating phases and symplectic topology. 51. Chaperon's method and the theorem Of ConleyZehnder. 52. Generating phases and symplectic geometry. 
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 ConleyZehnderMorse 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. 
Note 
Print version record. 
ISBN 
9789812810762 (electronic bk.) 

9812810765 (electronic bk.) 

9789810205898 

9810205899 
OCLC # 
269468913 
Additional Format 
Print version: Golé, Christophe. Symplectic twist maps. Singapore ; River Edge, NJ : World Scientific, ©2001 9789810205898 (DLC) 2002284360 (OCoLC)48960458 
