Ergodic optimization for generic continuous functions
Ergodic optimization for generic continuous functions
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DOI：
10.3934/dcds.2010.27.383
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发表时间：
2010-02
影响因子：
1.1
通讯作者：
I. Morris
中科院分区：
文献类型：
--
作者：
I. Morris
给定一个在动力系统的相空间上定义的实值连续函数 $f$，如果不变测度使 $f$ 在所有不变测度集合上的积分最大化，则该不变测度被称为最大化。扩展 Bousch、Jenkinson 和 Bremont 的结果，我们表明属于连续函数残差子集的函数的遍历最大化测度可以被表征为属于遍历测度的残差子集的那些测度。
Given a real-valued continuous function $f$ defined on the phase space of a dynamical system, an invariant measure is said to be maximizing if it maximises the integral of $f$ over the set of all invariant measures. Extending results of Bousch, Jenkinson and Bremont, we show that the ergodic maximizing measures of functions belonging to a residual subset of the continuous functions may be characterised as those measures which belong to a residual subset of the ergodic measures.