加权拓扑熵的两种定义之比较
Comparison of two approaches to weighted topological entropy
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中文总结 AI 辅助
本文比较了加权拓扑熵的Feng--Huang与覆盖定义，证明在非不变子集上Feng--Huang熵不超过覆盖熵，且证明不依赖测度论，为相对加权变分原理提供新视角。
中文摘要 AI 辅助
我们比较了动力系统间等变连续映射的加权拓扑熵的Feng--Huang定义与覆盖定义。这两种量在整体空间上通过变分原理是一致的，但在非不变子集上则未必一致。我们证明了在不假设不变性的情况下，Feng--Huang熵在每个子集上均以覆盖熵为上界。该证明不依赖于测度论。我们的主要结果为两个相对加权变分原理提供了新的视角。
英文摘要
We compare the Feng--Huang and covering definitions of weighted topological entropy for equivariant continuous maps between dynamical systems. The two quantities agree on the whole space by their variational principles, but need not agree on non-invariant subsets. We prove that the Feng--Huang entropy is bounded above by the covering entropy on every subset, without assuming invariance. The proof does not rely on measure theory. Our main result provides a new perspective on the two relative weighted variational principles.
发表机构
- Department of Mathematics, Kyoto University（京都大学数学系）
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