Quantitative recurrence properties for group actions

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Abstract

We generalized Boshernitzan's quantitative recurrence theorem to general group actions. Let (X, d) be a metric space with a finite measure and G be a countable group acting on (X, d). Assume that the action of G on (X, d) is measure preserving and let Fn ⊂ G be a sequence with |F n| ↑ ∞ and put . Then we have for almost every x, where α is the Hausdorff dimension of (X, d).

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalNonlinearity
Volume22
Issue number1
DOIs
StatePublished - 1 Jan 2009

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