Geodesic
Local dimensions for Poincaré recurrences
Afraimovich, Valentin1 ; Chazottes, Jean-René1 ; Saussol, Benoît2
1 IICO-UASLP, A. Obregon 64, San Luis Potosi SLP, 78210 Mexico
2 Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 64-74.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-00-00082-2

Afraimovich, Valentin 1 ; Chazottes, Jean-René 1 ; Saussol, Benoît 2

1 IICO-UASLP, A. Obregon 64, San Luis Potosi SLP, 78210 Mexico
2 Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal 
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Afraimovich, Valentin; Chazottes, Jean-René; Saussol, Benoît. Local dimensions for Poincaré recurrences. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 64-74. doi : 10.1090/S1079-6762-00-00082-2. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-00-00082-2/

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