Weighted topological pressure revisited

Nima Alibabaei

Weighted topological pressure revisited

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arxiv 2307.16772 v1 pith:HAOKJEFY submitted 2023-07-31 math.DS

Nima Alibabaei This is my paper · ORCID

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keywords pressureprincipletopologicalvariationalweighteddimensionentropysets

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Feng--Huang (2016) introduced weighted topological entropy and pressure for factor maps between dynamical systems and established its variational principle. Tsukamoto (2022) redefined those invariants quite differently for the simplest case and showed via the variational principle that the two definitions coincide. We generalize Tsukamoto's approach, redefine the weighted topological entropy and pressure for higher dimensions, and prove the variational principle. Our result allows for an elementary calculation of the Hausdorff dimension of affine-invariant sets such as self-affine sponges and certain sofic sets that reside in Euclidean space of arbitrary dimension.

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Mean dimension theory for infinite dimensional Bedford-McMullen sponges
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For Bedford-McMullen sponge systems with r coordinates, the metric mean dimension is a weighted sum of topological entropies of projections, and the mean Hausdorff dimension equals a weighted topological entropy divid...

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