New approach to weighted topological entropy and pressure
New approach to weighted topological entropy and pressure
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DOI：
10.1017/etds.2021.173
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发表时间：
2021-08
影响因子：
0.9
通讯作者：
M. Tsukamoto
中科院分区：
文献类型：
--
作者：
M. Tsukamoto
基于自仿射地毯和海绵的分形几何特征，冯和黄[J]。数学。应用力学，106(9)(2016)，411-452]引入了动态系统间因子映射的加权拓扑熵和压力，并证明了它们的变分原理。我们为这一理论引入了一种新的方法。我们对加权拓扑熵和压力的新定义与冯和黄的原始定义有很大的不同。这两个定义的等价性似乎非常重要。它们的等价性可以看作是贝德福德-麦克马伦地毯维度公式在纯拓扑学方面的推广。
Abstract Motivated by fractal geometry of self-affine carpets and sponges, Feng and Huang [J. Math. Pures Appl. 106(9) (2016), 411–452] introduced weighted topological entropy and pressure for factor maps between dynamical systems, and proved variational principles for them. We introduce a new approach to this theory. Our new definitions of weighted topological entropy and pressure are very different from the original definitions of Feng and Huang. The equivalence of the two definitions seems highly non-trivial. Their equivalence can be seen as a generalization of the dimension formula for the Bedford–McMullen carpet in purely topological terms.