Dimension and hitting time in rapidly mixing systems
type: Item
instance of: scholarly article
title: Dimension and hitting time in rapidly mixing systems
zbMATH Open document ID: 1134.37004
author: Stefano Galatolo
published in: Mathematical Research Letters
publication date: 2008-03-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0611911
review text: We prove that if a system has superpolynomial (faster than any power law) decay of correlations then the time \(\tau_r(x, x_0)\) needed for a typical point \(x\) to enter for the first time a ball \(B(x_0, r)\) centered in \(x_0\), with small radius \(r\) scales as the local dimension at \(x_0\), i.e. \[ \lim_{r\to 0}\;\frac{\log \tau_r(x, x_0)}{-\log r}=d_\mu(x_0). \] This result is obtained by proving a kind of dynamical Borel-Cantelli lemma which holds also in systems having polynomial decay of correlations.
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 5243855
zbMATH Keywords: dynamical Borel-Cantelli lemma
zbMATH Keywords: systems having polynomial decay of correlations
zbMATH Keywords: ergodic systems
MaRDI profile type: Publication
arXiv ID: math/0611911
DOI: 10.4310/MRL.2007.V14.N5.A8
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description: scientific article