Hitting times distribution and extreme value laws for semi-flows

Maria José Pacifico; Fan Yang

doi:10.3934/dcds.2017255

Article Contents

2017, Volume 37, Issue 11: 5861-5881. Doi: 10.3934/dcds.2017255

This issue Previous Article Estimating the fractal dimension of sets determined by nonergodic parameters Next Article Visco-Energetic solutions to one-dimensional rate-independent problems

Hitting times distribution and extreme value laws for semi-flows

Maria José Pacifico and
Fan Yang^,

Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil

* Corresponding author: Fan Yang
* Corresponding author: Fan Yang

Received: September 2016

Revised: June 2017

Published: October 2017

Maria José Pacifico is partially supported by CNPq, FAPERJ.
Fan Yang is partially supported by CAPES

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Abstract

For flows whose return map on a cross section has sufficient mixing property, we show that the hitting time distribution of the flow to balls is exponential in limit. We also establish a link between the extreme value distribution of the flow and its hitting time distribution, generalizing a previous work by Freitas et al in the discrete time case. Finally we show that for maps that can be modeled by Young's tower with polynomial tail, the extreme value laws hold.

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Mathematics Subject Classification: Primary: 37A05, 37A50, 37C10; Secondary: 60F99.

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References

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