Hamilton-Jacobi method for a simple resonance

Details Hamilton-Jacobi method for a simple resonance Hamilton-Jacobi method for a simple resonance

2003-05-09

arxiv.org/abs/math/0305143v1

Mathematics

Dynamical Systems

40 pages

Scientific paper

It is well known that a generic small perturbation of a Liouville-integrable Hamiltonian system causes breakup of resonant and near-resonant invariant tori. A general approach to the simple resonance case in the convex real-analytic setting is developed, based on a new technique for solving the Hamilton-Jacobi equation. It is shown that a generic perturbation creates in the core of a resonance a partially hyperbolic lower-dimensional invariant torus, whose Lagrangian stable and unstable manifolds, described as global solutions of the Hamilton-Jacobi equation, split away from this torus at exponentially small angles. Optimal upper bounds with best constants are obtained for exponentially small splitting in the general case.

Affiliated with

Also associated with

No associations

Rating

Hamilton-Jacobi method for a simple resonance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hamilton-Jacobi method for a simple resonance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hamilton-Jacobi method for a simple resonance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719615