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Analyticity of dimensions for hyperbolic surface diffeomorphisms


Author: M. Pollicott
Journal: Proc. Amer. Math. Soc. 143 (2015), 3465-3474
MSC (2010): Primary 37D35, 37F35
Published electronically: April 28, 2015
MathSciNet review: 3348789
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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
Email: mpollic@maths.warwick.ac.uk

DOI: https://doi.org/10.1090/proc/12477
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
Article copyright: © Copyright 2015 American Mathematical Society