PreprintCC BY-NC-ND 4.0arXiv
Comparison of two approaches to weighted topological entropy
Abstract
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.
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BibTeX
@misc{tsukamoto2026comparison,
title = {{Comparison of two approaches to weighted topological entropy}},
author = {Masaki Tsukamoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25497},
eprint = {2609.25497},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25497},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Comparison of two approaches to weighted topological entropy
AU - Masaki Tsukamoto
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25497
UR - https://arxiv.org/abs/2609.25497
AB - 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.
ER -