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Local dimensions for Poincaré recurrences
Author(s):
Valentin
Afraimovich;
Jean-René
Chazottes;
Benoît
Saussol
Journal:
Electron. Res. Announc. Amer. Math. Soc.
6
(2000),
64-74.
MSC (2000):
Primary 37C45, 37B20
Posted:
September 11, 2000
MathSciNet review:
1777857
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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 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.
References:
-
- 1.
- V. Afraimovich, Pesin's dimension for Poincaré recurrences, Chaos 7 (1997), 12-20. MR 98c:58080
- 2.
- V. Afraimovich, J.-R. Chazottes, and B. Saussol, Pointwise dimensions for Poincaré recurrences associated with maps and special flows, in preparation.
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Additional Information:
Valentin
Afraimovich
Affiliation:
IICO-UASLP, A. Obregon 64, San Luis Potosi SLP, 78210 Mexico
Email:
valentin@cactus.iico.uaslp.mx
Jean-René
Chazottes
Affiliation:
IICO-UASLP, A. Obregon 64, San Luis Potosi SLP, 78210 Mexico
Email:
jeanrene@cpt.univ-mrs.fr
Benoît
Saussol
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
Email:
saussol@math.ist.utl.pt
DOI:
10.1090/S1079-6762-00-00082-2
PII:
S 1079-6762(00)00082-2
Received by editor(s):
March 31, 2000
Posted:
September 11, 2000
Communicated by:
Svetlana Katok
Copyright of article:
Copyright
2000,
American Mathematical Society
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