Point-to-set principles in dynamical systems

Emma Dinowitz

arXiv:2607.21976v1 Primary: math.DS Secondary: cs.IT, math.LO, math.MG

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.

Disclosure

“A.20. The second is the conjunction of Lemma A.18 (dimBSP ≤ Dimsep BS ) and Lemma A.17 (Dimsep BS ≤ dimBSP ). B Declarations The large language models Claude Opus 4 and Fable 5 were used extensively in the creation of this paper, in the drafting, outlining, proof reading, and editing phases of writing the paper. References [BG13] Keith Burns and Katrin Gelfert. “Lyapunov spectrum f”
PDF page 52

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Verified: 2026-08-23T19:04:26.003776Z

Structural counts

Pages 53 pdf

Theorems 16 pdf fallback

Lemmas 40 pdf fallback

Propositions 0 pdf fallback

Corollaries 4 pdf fallback

Definitions 30 pdf fallback

Displayed equations 454 pdf fallback

Bibliography entries 2 pdf fallback

Appendix pages 46 estimated

Count notes

arXiv source was unavailable; PDF-text fallbacks were used.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.