Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians
Dynamical Systems
2015-06-12 v1
Abstract
This paper is a sequel to "Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.
Keywords
Cite
@article{arxiv.1212.1275,
title = {Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians},
author = {Abed Bounemoura},
journal= {arXiv preprint arXiv:1212.1275},
year = {2015}
}