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A symbolic characterization of the horseshoe locus in the Henon family for publication
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Bedford, Eric and Smillie, John (2017) A symbolic characterization of the horseshoe locus in the Henon family for publication. Ergodic Theory and Dynamical Systems, 37 (5). pp. 1389-1412. doi:10.1017/etds.2015.113 ISSN 0143-3857.
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WRAP_Smillie_0870007-ma-200116-bedfordsmilliesymbolichorseshoe-revised1.pdf - Accepted Version - Requires a PDF viewer. Download (1616Kb) | Preview |
Official URL: http://dx.doi.org/10.1017/etds.2015.113
Abstract
We consider the family of quadratic Hénon diffeomorphisms of the plane R2. A map will be said to be a ‘horseshoe’ if its restriction to the non-wandering set is hyperbolic and conjugate to the full 2-shift. We give a criterion for being a horseshoe based on an auxiliary coding which describes positions of points relative to the stable manifold of one of the fixed points. In addition we describe the topological conjugacy type of maps on the boundary of the horseshoe locus. We use complex techniques and we work with maps in a parameter region which is a two-dimensional analog of the familiar ‘1/2-wake’ for the quadratic family pc(z)=z2.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Library of Congress Subject Headings (LCSH): | Ergodic Theory, Entropy , Nonlinear theories | ||||||||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||||||||
Publisher: | Cambridge University Press | ||||||||||
ISSN: | 0143-3857 | ||||||||||
Official Date: | August 2017 | ||||||||||
Dates: |
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Volume: | 37 | ||||||||||
Number: | 5 | ||||||||||
Page Range: | pp. 1389-1412 | ||||||||||
DOI: | 10.1017/etds.2015.113 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Date of first compliant deposit: | 16 June 2016 | ||||||||||
Date of first compliant Open Access: | 8 September 2016 |
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