Rare events for Cantor target sets
Dynamical Systems
2019-03-19 v1
Abstract
We study the existence of limiting laws of rare events corresponding to the entrance of the orbits on certain target sets in the phase space. The limiting laws are obtained when the target sets shrink to a Cantor set of zero Lebesgue measure. We consider both the presence and absence of clustering, which is detected by the Extremal Index, which turns out to be very useful to identify the compatibility between the dynamics and the fractal structure of the limiting Cantor set. The computation of the Extremal Index is connected to the box dimension of the intersection between the Cantor set and its iterates.
Cite
@article{arxiv.1903.07200,
title = {Rare events for Cantor target sets},
author = {Ana Cristina Moreira Freitas and Jorge Milhazes Freitas and Fagner B. Rodrigues and Jorge Valentim Soares},
journal= {arXiv preprint arXiv:1903.07200},
year = {2019}
}