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arXiv · 2108.03795

New approach to weighted topological entropy and pressure

Masaki Tsukamoto
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Abstract

Motivated by fractal geometry of self-affine carpets and sponges, Feng--Huang (2016) 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--Huang. The equivalence of the two definitions seems highly nontrivial. Their equivalence can be seen as a generalization of the dimension formula for the Bedford--McMullen carpet in purely topological terms.

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Masaki Tsukamoto. 2021-08-09. New approach to weighted topological entropy and pressure. https://arxiv.org/abs/2108.03795

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