Article contents
Hyperbolic periodic orbits and Mather sets in certain symmetric cases
Published online by Cambridge University Press: 03 July 2006
Abstract
We consider a $C^\infty$ Lagrangian function $L: T^*M\rightarrow \mathbb{R}$ which is superlinear and convex in the fibers and has one antisymplectic symmetry. We prove that:
in every energy level strictly above the critical one, there exists a Mather set which is the union of some periodic orbits;
for $L$ generic, these orbits are hyperbolic;
on the torus, these orbits have one homoclinic orbit.
- Type
- Research Article
- Information
- Copyright
- 2006 Cambridge University Press
- 2
- Cited by