Manifolds on the verge of a hyperbolicity breakdown.

Abstract

We study numerically the disappearance of normally hyperbolic invariant tori in quasiperiodic systems and identify a scenario for their breakdown. In this scenario, the breakdown happens because two invariant directions of the transversal dynamics come close to each other, losing their regularity. On the other hand, the Lyapunov multipliers associated with the invariant directions remain more or less constant. We identify notable quantitative regularities in this scenario, namely that the minimum angle between the two invariant directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws seem to be universal.

Extracted Key Phrases

Cite this paper

@article{Haro2006ManifoldsOT, title={Manifolds on the verge of a hyperbolicity breakdown.}, author={A. Haro and Rafael de la Llave}, journal={Chaos}, year={2006}, volume={16 1}, pages={013120} }