Qualitative Theory of Dynamical Systems ( IF 1.4 ) Pub Date : 2021-05-18 , DOI: 10.1007/s12346-021-00485-7 Andrzej Biś , Dikran Dikranjan , Anna Giordano Bruno , Luchezar Stoyanov
We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological entropy introduced by Hofmann and Stoyanov (Adv Math 115:54–98, 1995). We analyze its basic properties and its relation with the classical metric entropy. In the case of semigroup actions on compact metric spaces we compare the receptive metric entropy with the receptive topological entropy looking for a Variational Principle. With this aim we propose several characterizations of the receptive topological entropy. Finally we introduce a receptive local metric entropy inspired by a notion by Bowen generalized in the classical setting of amenable group actions by Zheng and Chen, and we prove partial versions of the Brin–Katok Formula and the local Variational Principle.
中文翻译:
半群动作的度量对拓扑接受熵
我们研究了概率空间上半群作用的接受度量熵,这是受到霍夫曼和斯托扬诺夫提出的类似拓扑熵概念的启发(高级数学115:54-98,1995)。我们分析了它的基本性质及其与经典度量熵的关系。对于紧凑度量空间上的半群作用,我们将接受度量熵与接受拓扑熵进行比较,以寻找变分原理。为此,我们提出了接收拓扑熵的几个特征。最后,我们引入了鲍恩(Bowen)的概念的启发性的接受局部度量熵,该熵在郑和陈的顺应性群体动作的经典背景中得到了概括,并且证明了布林-卡托克公式和局部变分原理的部分形式。