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Mathematics > Dynamical Systems

arXiv:1808.00933 (math)
[Submitted on 2 Aug 2018 (v1), last revised 4 May 2019 (this version, v2)]

Title:Pressure, Poincaré series and box dimension of the boundary

Authors:Godofredo Iommi, Aníbal Velozo
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Abstract:In this note we prove two related results. First, we show that for certain Markov interval maps with infinitely many branches the upper box dimension of the boundary can be read from the pressure of the geometric potential. Secondly, we prove that the box dimension of the set of iterates of a point in H^n with respect to a parabolic subgroup of isometries equals the critical exponent of the Poincare series of the associated group. This establishes a relationship between the entropy at infinity and dimension theory.
Comments: Introduction has been rewritten. Comments welcome
Subjects: Dynamical Systems (math.DS)
Cite as: arXiv:1808.00933 [math.DS]
  (or arXiv:1808.00933v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1808.00933
Journal reference: Nonlinearity 34 (2021) 3936-3952
Related DOI: https://doi.org/10.1088/1361-6544/abfecf

Submission history

From: Anibal Velozo [view email]
[v1] Thu, 2 Aug 2018 17:34:44 UTC (18 KB)
[v2] Sat, 4 May 2019 18:35:02 UTC (23 KB)
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