Centralizers of partially hyperbolic diffeomorphisms in dimension 3

Thomas Barthelmé; Andrey Gogolev

doi:10.3934/dcds.2021044

Article Contents

2021, Volume 41, Issue 9: 4477-4484. Doi: 10.3934/dcds.2021044

This issue Previous Article Pointwise gradient bounds for a class of very singular quasilinear elliptic equations Next Article Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity

Centralizers of partially hyperbolic diffeomorphisms in dimension 3

Thomas Barthelmé^1, and
Andrey Gogolev^2, ,

1.
Queen's University, Kingston, Ontario
2.
Ohio State University, Columbus, Ohio

^* Corresponding author: Andrey Gogolev
^* Corresponding author: Andrey Gogolev

Received: December 31, 2020

Revised: December 31, 2020

Early access: March 2021

Published: September 2021

The first author was partially supported by the NSERC (Funding reference number RGPIN-2017-04592). The second author was partially supported by NSF DMS-1823150

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Abstract

In this note we describe centralizers of volume preserving partially hyperbolic diffeomorphisms which are homotopic to identity on Seifert fibered and hyperbolic 3-manifolds. Our proof follows the strategy of Damjanovic, Wilkinson and Xu [10] who recently classified the centralizer for perturbations of time-$ 1 $ maps of geodesic flows in negative curvature. We strongly rely on recent classification results in dimension 3 established in [5,6].

Keywords:

Partially hyperbolic diffeomorphisms,
centralizer.

Mathematics Subject Classification: Primary: 37D30.

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References

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