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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Analyticity of dimensions for hyperbolic surface diffeomorphisms
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by M. Pollicott PDF
Proc. Amer. Math. Soc. 143 (2015), 3465-3474 Request permission

Abstract:

In this note we give a simple proof that the Hausdorff dimension of the basic set for a real analytic Smale horseshoe map depends analytically on the transformation. This method is based on the use of dynamical zeta functions. We prove analogous statements for the value of the pointwise dimension of the measure of maximal entropy and then use this to address an interesting question raised by Damanik and Gorodetski.
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Additional Information
  • M. Pollicott
  • Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
  • MR Author ID: 140805
  • Email: mpollic@maths.warwick.ac.uk
  • Received by editor(s): May 10, 2013
  • Received by editor(s) in revised form: November 30, 2013
  • Published electronically: April 28, 2015
  • Communicated by: Nimish Shah
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3465-3474
  • MSC (2010): Primary 37D35, 37F35
  • DOI: https://doi.org/10.1090/proc/12477
  • MathSciNet review: 3348789