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Partially hyperbolic surface endomorphisms

Part of: Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory Differential topology

Published online by Cambridge University Press:  03 September 2019

LAYNE HALL  and
ANDY HAMMERLINDL
LAYNE HALL
Affiliation:
School of Mathematical Sciences, Monash University, Victoria3800, Australia email layne.hall@monash.edu, andy.hammerlindl@monash.edu
ANDY HAMMERLINDL
Affiliation:
School of Mathematical Sciences, Monash University, Victoria3800, Australia email layne.hall@monash.edu, andy.hammerlindl@monash.edu
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Abstract

We prove that a class of weakly partially hyperbolic endomorphisms on $\mathbb{T}^{2}$ are dynamically coherent and leaf conjugate to linear toral endomorphisms. Moreover, we give an example of a partially hyperbolic endomorphism on $\mathbb{T}^{2}$ which does not admit a centre foliation.

Keywords

partial hyperbolicitynon-invertible dynamicsdynamical coherence

MSC classification

Primary: 37D30: Partially hyperbolic systems and dominated splittings
Secondary: 37C05: Smooth mappings and diffeomorphisms 57R30: Foliations; geometric theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 1 , January 2021 , pp. 272 - 282
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Copyright
© Cambridge University Press, 2019

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