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Upper semi-continuity of entropy in non-compact settings
Mathematical Research Letters ( IF 1 ) Pub Date : 2020-01-01 , DOI: 10.4310/mrl.2020.v27.n4.a4 Godofredo Iommi 1 , Mike Todd 2 , Aníbal Velozo 3
Mathematical Research Letters ( IF 1 ) Pub Date : 2020-01-01 , DOI: 10.4310/mrl.2020.v27.n4.a4 Godofredo Iommi 1 , Mike Todd 2 , Aníbal Velozo 3
Affiliation
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive entropy diffeomorphisms on compact manifolds, are given. We also discuss the related problem of existence of measures of maximal entropy.
中文翻译:
非紧致环境中熵的上半连续性
我们证明了有限熵的可数马尔可夫位移的熵图在遍历测度下是上半连续的。请注意,相空间是非紧凑的。给出了可以通过这些移位编码的系统的应用,例如紧流形上的正熵微分同胚。我们还讨论了最大熵度量存在的相关问题。
更新日期:2020-01-01
中文翻译:
非紧致环境中熵的上半连续性
我们证明了有限熵的可数马尔可夫位移的熵图在遍历测度下是上半连续的。请注意,相空间是非紧凑的。给出了可以通过这些移位编码的系统的应用,例如紧流形上的正熵微分同胚。我们还讨论了最大熵度量存在的相关问题。