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No round wandering domains for $C^{1}$-diffeomorphisms of tori

Published online by Cambridge University Press:  10 April 2018

SERGEI MERENKOV
SERGEI MERENKOV*
Affiliation:
Department of Mathematics, City College of New York and CUNY Graduate Center, New York, NY 10031, USA email smerenkov@ccny.cuny.edu
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Abstract

We prove that if $n\geq 2$, then there is no $C^{1}$-diffeomorphism $f$ of the $n$-torus such that $f$ is semi-conjugate to a minimal translation and its wandering domains are geometric balls. This improves a recent result of Navas, who proved it assuming $C^{n+1}$ regularity of $f$.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 3127 - 3135
Copyright
© Cambridge University Press, 2018 

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