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Codimension one compact center foliations are uniformly compact

Part of: Dynamical systems with hyperbolic behavior Differential topology

Published online by Cambridge University Press:  13 March 2019

VERÓNICA DE MARTINO  and
SANTIAGO MARTINCHICH
VERÓNICA DE MARTINO
Affiliation:
CMAT, Facultad de Ciencias, Universidad de la República, Uruguay email vdemartino@cmat.edu.uy, smartinchich@cmat.edu.uy
SANTIAGO MARTINCHICH
Affiliation:
CMAT, Facultad de Ciencias, Universidad de la República, Uruguay email vdemartino@cmat.edu.uy, smartinchich@cmat.edu.uy
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Abstract

Let $f:M\rightarrow M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded in $M$.

Keywords

partial hyperbolicitycompact foliationsskew productsclassification

MSC classification

Primary: 37D30: Partially hyperbolic systems and dominated splittings
Secondary: 57R30: Foliations; geometric theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 9 , September 2020 , pp. 2349 - 2367
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Copyright
© Cambridge University Press, 2019

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