Equilibrium measures for maps with inducing schemes
Equilibrium measures for maps with inducing schemes
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具有诱导方案的地图的均衡测度
DOI：
10.3934/jmd.2008.2.397
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发表时间：
2006
影响因子：
1.1
通讯作者：
S. Senti
中科院分区：
文献类型：
--
作者：
Y. Pesin;S. Senti
本文引入了紧致拓扑空间I中一类具有诱导格式的连续映射f，并描述了与之相关的塔结构。然后，我们建立了一个抽象的形式主义，即，定义了一类关于I的实值势函数，它允许一个唯一的平衡测度，使得某类不变测度的自由能最小化。我们还描述了平衡测度的遍历性质，包括相关性的衰减和中心极限定理。我们的结果适用于某些具有临界点和/或奇异点的区间映射（包括一些单峰和多峰映射）以及势函数<$t =−t log| D f|其中t ∈（t0，t1），其中t0 < 1< t1。在S-单峰映射的特殊情况下，我们证明了可以选择t0 < 0，并且所考虑的测度类由所有不变的Borel概率测度组成。
We introducea class of continuousmaps f of a compact topologi- cal space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamicformalism, i.e., de- scribe a class of real-valued potential functions ϕ on I, which admit a unique equilibrium measure ¹ ϕ minimizing the free energy for a certain class of in- variant measures. We also describe ergodic properties of equilibrium mea- sures, including decay of correlation and the Central Limit Theorem. Our re- sults apply to certain maps of the interval with critical points and/or singular- ities (including some unimodal and multimodal maps) and to potential func- tions ϕt =−t log|d f | with t ∈(t0,t1) for some t0 < 1< t1. In theparticularcase of S-unimodal maps we show that one can choose t0 < 0 and that the class of measures under consideration consists of all invariant Borel probability mea- sures.