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Polynomial decay of correlations in linked-twist maps

Published online by Cambridge University Press:  04 April 2013

J. SPRINGHAM  and
R. STURMAN
J. SPRINGHAM
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK email uniquealphabeticcombination@gmail.comr.sturman@leeds.ac.uk
R. STURMAN
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK email uniquealphabeticcombination@gmail.comr.sturman@leeds.ac.uk
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Abstract

Linked-twist maps are area-preserving, piecewise diffeomorphisms, defined on a subset of the torus. They are non-uniformly hyperbolic generalizations of the well-known Arnold cat map. We show that a class of canonical examples have polynomial decay of correlations for $\alpha $-Hölder observables, of order $1/ n$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 5 , October 2014 , pp. 1724 - 1746
Copyright
Copyright ©2013 Cambridge University Press 

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