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 language | English |
|---|---|
| Pages (from-to) | 1-9 |
| Number of pages | 9 |
| Journal | Nonlinearity |
| Volume | 22 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2009 |