Analyticity of dimensions for hyperbolic surface diffeomorphisms
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- by M. Pollicott
- Proc. Amer. Math. Soc. 143 (2015), 3465-3474
- DOI: https://doi.org/10.1090/proc/12477
- Published electronically: April 28, 2015
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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.References
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Bibliographic 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