Point-to-set principles in dynamical systems

2026/07/24 by Emma Dinowitz
Computer Science · Mathematics · #math.DS #cs.IT #math.IT #math.LO #math.MG

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Abstract

In analogy to the point-to-set principle for Hausdorff and packing dimension of Lutz, Lutz, and Mayordomo, we develop a Kolmogorov complexity point-to-set principle framework for upper and lower topological pressure and BS dimension in dynamical systems (and by extension for upper and lower entropy). As a demonstration of this framework we expand upon the Bowen pressure equation results of Climenhaga, as well as prove a pointwise version of the Bowen pressure equation.

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