Geodesic
The recurrence dimension for piecewise monotonic maps of the interval
Hofbauer, Franz1
1 Fakultät für Mathematik Universität Wien Nordbergstraße 15 A 1090 Wien, Austria
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 439-449

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We investigate a weighted version of Hausdorff dimension introduced by V. Afraimovich, where the weights are determined by recurrence times. We do this for an ergodic invariant measure with positive entropy of a piecewise monotonic transformation on the interval [0,1], giving first a local result and proving then a formula for the dimension of the measure in terms of entropy and characteristic exponent. This is later used to give a relation between the dimension of a closed invariant subset and a pressure function.

Classification : 37E05, 37C45, 28A80, 37B40, 28A78

Hofbauer, Franz 1

1 Fakultät für Mathematik Universität Wien Nordbergstraße 15 A 1090 Wien, Austria 
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     title = {The recurrence dimension for piecewise monotonic maps of the interval},
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Hofbauer, Franz. The recurrence dimension for piecewise monotonic maps of the interval. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 439-449. http://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_3_439_0/