Optical Hamiltonians and symplectic twist maps
Dynamical Systems
2009-09-25 v1 Symplectic Geometry
Abstract
This paper concentrates on optical Hamiltonian systems of , i.e. those for which is a positive definite matrix, and their relationship with symplectic twist maps. We present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems. The novelty of these results resides in the fact that no explicit asymptotic condition is imposed on the system. We also present a theorem of suspension by Hamiltonian systems for the class of symplectic twist map that emerges in our study. Finally, we extend our results to manifolds of negative curvature.
Cite
@article{arxiv.math/9210228,
title = {Optical Hamiltonians and symplectic twist maps},
author = {Christopher Golé},
journal= {arXiv preprint arXiv:math/9210228},
year = {2009}
}