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smooth models

Ergodic Theory and Dynamical Systems (1)

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Smooth models for certain fibered partially hyperbolic systems
Part of
- Smooth dynamical systems: general theory
- Dynamical systems with hyperbolic behavior
MEG DOUCETTE
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 8 / August 2024

Published online by Cambridge University Press:

13 November 2023, pp. 2173-2198

Print publication:

August 2024
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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.