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Non-differentiable irrational curves for $C^1$ twist map

Part of: Low-dimensional dynamical systems

Published online by Cambridge University Press:  02 December 2021

ARTUR AVILA  and
BASSAM FAYAD Open the ORCID record for BASSAM FAYAD [Opens in a new window]
ARTUR AVILA
Affiliation:
Institut fϋr Mathematik Universität Zϋrich, Winterthurerstrasse 190, CH-8057Zϋrich, Switzerland
BASSAM FAYAD*
Affiliation:
Institut de Mathématiques de Jussieu-Paris Rive Gauche, 58-56, avenue de France, Boite Courrier 7012, 75205Paris Cedex 13, France
*
e-mail: bassam.fayad@imj-prg.fr
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Abstract

We construct a $C^1$ symplectic twist map g of the annulus that has an essential invariant curve $\Gamma $ such that $\Gamma $ is not differentiable and g restricted to $\Gamma $ is minimal.

Keywords

twist mapsinvariant curvesBirkhoff theory

MSC classification

Primary: 37E40: Twist maps 37E10: Maps of the circle
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 2: Anatole Katok Memorial Issue Part 1: Special Issue of Ergodic Theory and Dynamical Systems , February 2022 , pp. 491 - 499
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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