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Advanced Series in Nonlinear Dynamics - Vol. 18
SYMPLECTIC TWIST MAPS
Global Variational Techniques
by Christophe Golé (Smith College, USA)
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.
Contents:
- Twist Maps of the Annulus
- The Aubry-Mather Theorem
- Ghost
Circles
- Symplectic Twist Maps
- Periodic Orbits for Symplectic Twist Maps of Tn x IRn
- Invariant Manifolds
- Hamiltonian Systems vs. Twist Maps
- Periodic Orbits for Hamiltonian Systems
- Generalizations of the Aubry-Mather Theorem
- Generating Phases and Symplectic Topology
Readership: Pure and applied mathematicians and physicists.
"... this book constitutes a fundamental monograph on the subject and gives a beautiful treatment of many results in the area that previously have only been accessible in original research papers."
| 324pp |
Pub. date: Nov 2001 |
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