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Positive topological entropy for monotone recurrence relations

Published online by Cambridge University Press:  30 June 2014

LI GUO ,
XUE-QING MIAO ,
YA-NAN WANG  and
WEN-XIN QIN
LI GUO
Affiliation:
Department of Mathematics, Soochow University, Suzhou, 215006, China email [email protected]
XUE-QING MIAO
Affiliation:
Department of Mathematics, Soochow University, Suzhou, 215006, China email [email protected]
YA-NAN WANG
Affiliation:
Department of Mathematics, Soochow University, Suzhou, 215006, China email [email protected]
WEN-XIN QIN
Affiliation:
Department of Mathematics, Soochow University, Suzhou, 215006, China email [email protected]
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Abstract

We associate the topological entropy of monotone recurrence relations with the Aubry–Mather theory. If there exists an interval $[{\it\rho}_{0},{\it\rho}_{1}]$ such that, for each ${\it\omega}\in ({\it\rho}_{0},{\it\rho}_{1})$, all Birkhoff minimizers with rotation number ${\it\omega}$ do not form a foliation, then the diffeomorphism on the high-dimensional cylinder defined via the monotone recurrence relation has positive topological entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 6 , September 2015 , pp. 1880 - 1901
Copyright
© Cambridge University Press, 2014 

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