Â鶹ӰԺ

Effect of islands in the diffusive properties of the Chirikov standard map

Date and time:Ìý

Thursday, September 3, 2015 - 2:00pm

³¢´Ç³¦²¹³Ù¾±´Ç²Ô:Ìý

ECCR 257

´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý

The Chirikov standard map is a paradigmatic model. It exhibits, for large values of the parameter k, a seemingly fully chaotic phase space, except for some moderate size islands whose area is O(k^{-2}), and other extremely tiny islands. Some of these moderate size islands are accelerator modes, which play a decisive role in the overall diffusive properties of the y component under the iteration ofmthe standard map, when considered in the cylinder.

In this talk we review, based on massive, long term, numerical simulations, the statistical properties of the diffusion of the standard map in the presence of the accelerator mode islands, in terms of available limit models of their dynamics. In particular we stress out the role played by the breakdown of invariant curves around these islands and how this can be interpreted thanks to a suitable analysis of the quadratic Hénon map.

This is a joint work with C. Simó and A. Vieiro.