Ergodic optimization of super-continuous functions on shift spaces
Ergodic optimization of super-continuous functions on shift spaces
复制标题
移位空间上超连续函数的遍历优化
DOI：
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发表时间：
2011
影响因子：
0.9
通讯作者：
Jason Siefken
中科院分区：
文献类型：
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作者：
A. Quas;Jason Siefken
摘要遍历优化是寻找最大化给定函数积分的不变概率度量的过程。人们猜想，大多数函数是由周期轨道上支持的测度优化的，并且在几个可分空间中已被证明，开的稠密函数子集是通过周期轨道上支持的测度优化的。所有已知的正结果都是关于可分空间的。本文给出了不可分空间，全移位上的超连续函数空间的第一个正结果，其中经周期轨道测度优化的函数集包含一个开稠密子集。
Abstract Ergodic optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that ‘most’ functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive results have been for separable spaces. We give in this paper the first positive result for a non-separable space, the space of super-continuous functions on the full shift, where the set of functions optimized by periodic orbit measures contains an open dense subset.