2024
DOI: 10.3390/e26110979
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Bowen’s Formula for a Dynamical Solenoid

Andrzej Biś,
Wojciech Kozłowski,
Agnieszka Marczuk

Abstract: More than 50 years ago, Rufus Bowen noticed a natural relation between the ergodic theory and the dimension theory of dynamical systems. He proved a formula, known today as the Bowen’s formula, that relates the Hausdorff dimension of a conformal repeller to the zero of a pressure function defined by a single conformal map. In this paper, we extend the result of Bowen to a sequence of conformal maps. We present a dynamical solenoid, i.e., a generalized dynamical system obtained by backward compositions of a seq… Show more

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