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Classification of partially hyperbolic diffeomorphisms under some rigid conditions

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  22 October 2020

PABLO D. CARRASCO Open the ORCID record for PABLO D. CARRASCO [Opens in a new window] ,
ENRIQUE PUJALS  and
FEDERICO RODRIGUEZ-HERTZ
PABLO D. CARRASCO
Affiliation:
ICEx-UFMG, Avda. Presidente Antonio Carlos 6627, Belo Horizonte – MG, BR 31270-90, Brazil (e-mail: pdcarrasco@mat.ufmg.br)
ENRIQUE PUJALS
Affiliation:
CUNY Graduate Center, Room 4208, 365 Fifth Avenue, New York, NY 10016, USA (e-mail: epujals@gc.cuny.edu)
FEDERICO RODRIGUEZ-HERTZ
Affiliation:
Penn State, 227 McAllister Building, University Park, State College, PA 16802, USA (e-mail: hertz@math.psu.edu)
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Abstract

Consider a three-dimensional partially hyperbolic diffeomorphism. It is proved that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) an Anosov diffeomorphism, a (generalized) skew-product or the time-one map of an Anosov flow, thus recovering a well-known classification conjecture of the second author to this restricted setting.

Keywords

partial hyperbolicityrigiditythree manifolds

MSC classification

Primary: 37D30: Partially hyperbolic systems and dominated splittings
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 9 , September 2021 , pp. 2770 - 2781
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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