Slow polynomial mixing, dynamical Borel-Cantelli lemma and Hausdorff dimension of dynamical diophantine sets
Edouard Daviaud
TL;DR
This paper investigates the limits of the dynamical Borel-Cantelli lemma and determines the Hausdorff dimension of specific dynamical diophantine sets, providing optimality results in these areas.
Contribution
It introduces new optimality results for the dynamical Borel-Cantelli lemma and calculates the Hausdorff dimension of dynamical diophantine sets.
Findings
Established optimality results for the dynamical Borel-Cantelli lemma
Determined the Hausdorff dimension of certain dynamical diophantine sets
Provided new insights into the measure-theoretic properties of dynamical systems
Abstract
In this article, we establish optimality results regarding the dynamical Borel-Cantelli lemma and the the Hausdorff dimension of certain dynamical diophantine sets.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Advanced Topology and Set Theory