Abstract
Pointwise dimensions and spectra for measures associated with Poincaré recurrences are calculated for arbitrary weakly specified subshifts with positive entropy and for the corresponding special ows. It is proved that the Poincaré recurrence for a “typical” cylinder is asymptotically its length. Examples are provided which show that this is not true for some systems with zero entropy. Precise formulas for dimensions of measures associated with Poincaré recurrences are derived, which are comparable to Young's formula for the Hausdorff dimension of measures and Abramov's formula for the entropy of special ows.
| Original language | English |
|---|---|
| Pages (from-to) | 64-74 |
| Number of pages | 11 |
| Journal | Electronic Research Announcements of the American Mathematical Society |
| Volume | 6 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 11 Sept 2000 |
| Externally published | Yes |