The recurrence dimension for piecewise monotonic maps of the interval
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 4 (2005) no. 3, p. 439-449
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
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {3},
     year = {2005},
     pages = {439-449},
     zbl = {1170.37316},
     mrnumber = {2185864},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 4 (2005) no. 3, pp. 439-449. http://www.numdam.org/item/ASNSP_2005_5_4_3_439_0/

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