Displaying similar documents to “On the uniqueness of equilibrium states for piecewise monotone mappings”

Residuality of dynamical morphisms

R. Burton, M. Keane, Jacek Serafin (2000)

Colloquium Mathematicae

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We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.

Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations

Franz Hofbauer (2009)

Commentationes Mathematicae Universitatis Carolinae

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We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights...

The recurrence dimension for piecewise monotonic maps of the interval

Franz Hofbauer (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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...