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- Title
POSITIVE METRIC ENTROPY ARISES IN SOME NONDEGENERATE NEARLY INTEGRABLE SYSTEMS.
- Authors
DONG CHEN
- Abstract
The celebrated KAM theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a large measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws a lot of attention. In this paper we present a Lagrangian perturbation of the geodesic flow on a flat 3-torus. The perturbation is C∞ small but the flow has a positive measure of trajectories with positive Lyapunov exponent. The measure of this set is of course extremely small. Still, the flow has positive metric entropy. From this result we get positive metric entropy outside some KAM tori.
- Subjects
ENTROPY (Information theory); SYSTEMS theory; GEODESIC flows; NON-degenerate perturbation theory; LYAPUNOV exponents
- Publication
Journal of Modern Dynamics, 2017, Vol 11, p43
- ISSN
1930-5311
- Publication type
Article
- DOI
10.3934/jmd.2017003