Geometric Shadowing in Slow-Fast Hamiltonian Systems

Details Geometric Shadowing in Slow-Fast Hamiltonian Systems Geometric Shadowing in Slow-Fast Hamiltonian Systems

2009-05-19

arxiv.org/abs/0905.3087v2

Mathematics

Dynamical Systems

17 pages

Scientific paper

We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At $% \epsilon =0$ the slow dynamics is frozen. We assume that the frozen system (i.e. the unperturbed fast dynamics) has families of hyperbolic periodic orbits with transversal heteroclinics. For each periodic orbit we define an action $J.$ This action may be viewed as an action Hamiltonian (in the slow variables). It has been shown in (N. Br\"annstr\"om, V.Gelfreich (2008)) that there are orbits of the full dynamics which shadow any \emph{finite} combination of forward orbits of $J$ for a time $t=O(\epsilon^{-1})$. We introduce an assumption on the mutual relationship between the actions $J.$ This assumption enables us to shadow any continuous curve (of arbitrary length) in the slow phase space for any time. The slow dynamics shadows the curve as a purely geometrical object, thus the time on the slow dynamics has to be reparameterised.

Affiliated with

Also associated with

No associations

Rating

Geometric Shadowing in Slow-Fast Hamiltonian Systems 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 Geometric Shadowing in Slow-Fast Hamiltonian Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Shadowing in Slow-Fast Hamiltonian Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699790