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• W3100814861 startingPage "397" @default.
• W3100814861 abstract "We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions phi on I which admit unique equilibrium measures mu_phi minimizing the free energy for a certain class of measures. We also describe ergodic properties of equilibrium measures including decay of correlation and the Central Limit Theorem. Our results apply in particular to some one-dimensional unimodal and multimodal maps as well as to multidimensional nonuniformly hyperbolic maps admitting Young's tower. Examples of potential functions to which our theory applies include phi_t=-tlog|df| with tin(t_0, t_1) for some t_0<1<t_1. In the particular case of S-unimodal maps we show that one can choose t_0<0 and that the class of measures under consideration comprises all invariant Borel probability measures. Thus our results establish existence and uniqueness of both the measure of maximal entropy (by a different method than Hofbauer) and the absolutely continuous invariant measure extending results by Bruin and Keller for the parameters under consideration." @default.
• W3100814861 created "2020-11-23" @default.
• W3100814861 creator A5063584991 @default.
• W3100814861 creator A5079118474 @default.
• W3100814861 date "2008-01-01" @default.
• W3100814861 modified "2023-10-17" @default.
• W3100814861 title "Equilibrium measures for maps with inducing schemes" @default.
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• W3100814861 doi "https://doi.org/10.3934/jmd.2008.2.397" @default.
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