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Positive topological entropy for monotone recurrence relations

  • LI GUO (a1), XUE-QING MIAO (a1), YA-NAN WANG (a1) and WEN-XIN QIN (a1)

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.

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Positive topological entropy for monotone recurrence relations

  • LI GUO (a1), XUE-QING MIAO (a1), YA-NAN WANG (a1) and WEN-XIN QIN (a1)

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