Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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 flows. 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 flows.

Copyright 2000 American Mathematical Society

TeX source (37.4K)
DVI (52K)
PostScript (168.6K)

Article Info

• ERA Amer. Math. Soc. 06 (2000), pp. 64-74
• Publisher Identifier: S 1079-6762(00)00082-2
• 2000 Mathematics Subject Classification. Primary 37C45, 37B20
• Received by the editors March 31, 2000
• Posted on September 11, 2000
• Communicated by Svetlana Katok
• Comments (When Available)

Valentin Afraimovich

IICO-UASLP, A. Obregon 64, San Luis Potosi SLP, 78210 Mexico

E-mail address: valentin@cactus.iico.uaslp.mx

Jean-René Chazottes

IICO-UASLP, A. Obregon 64, San Luis Potosi SLP, 78210 Mexico

E-mail address: jeanrene@cpt.univ-mrs.fr

Benoît Saussol

Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal

E-mail address: saussol@math.ist.utl.pt