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 , 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.
Hofbauer, Franz 1
@article{ASNSP_2005_5_4_3_439_0,
author = {Hofbauer, Franz},
title = {The recurrence dimension for piecewise monotonic maps of the interval},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {439--449},
year = {2005},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {3},
mrnumber = {2185864},
zbl = {1170.37316},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2005_5_4_3_439_0/}
}
TY - JOUR AU - Hofbauer, Franz TI - The recurrence dimension for piecewise monotonic maps of the interval JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2005 SP - 439 EP - 449 VL - 4 IS - 3 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2005_5_4_3_439_0/ LA - en ID - ASNSP_2005_5_4_3_439_0 ER -
%0 Journal Article %A Hofbauer, Franz %T The recurrence dimension for piecewise monotonic maps of the interval %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2005 %P 439-449 %V 4 %N 3 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2005_5_4_3_439_0/ %G en %F ASNSP_2005_5_4_3_439_0
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. https://www.numdam.org/item/ASNSP_2005_5_4_3_439_0/
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