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Smooth models for certain fibered partially hyperbolic systems

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

Published online by Cambridge University Press:  13 November 2023

MEG DOUCETTE
MEG DOUCETTE*
Affiliation:
Department of Mathematics, University of Chicago, Chicago, USA
*
e-mail: mdoucette@uchicago.edu
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Abstract

We prove that under restrictions on the fiber, any fibered partially hyperbolic system over a nilmanifold is leaf conjugate to a smooth model that is isometric on the fibers and descends to a hyperbolic nilmanifold automorphism on the base. One ingredient is a result of independent interest generalizing a result of Hiraide: an Anosov homeomorphism of a nilmanifold is topologically conjugate to a hyperbolic nilmanifold automorphism.

Keywords

partial hyperbolicitysmooth modelsrigidityAnosov homeomorphisms

MSC classification

Primary: 37D30: Partially hyperbolic systems and dominated splittings
Secondary: 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 8 , August 2024 , pp. 2173 - 2198
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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