On the three-legged accessibility property

We show that certain types of the three-legged accessibility property of a partially hyperbolic diffeomorphism imply the existence of a unique minimal set for one strong foliation and the transitivity of the other one. In case the center dimension is one, we also give a criteria to obtain three-legg...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: Jana Rodriguez Hertz, Ures, Raúl
Format: Article
Language:English
Subjects:
Accessibility
Flow mapping
Isomorphism
Online Access:Get full text
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Summary:We show that certain types of the three-legged accessibility property of a partially hyperbolic diffeomorphism imply the existence of a unique minimal set for one strong foliation and the transitivity of the other one. In case the center dimension is one, we also give a criteria to obtain three-legged accessibility in a robust way. We show some applications of our results to the time-one map of Anosov flows, skew products and certain Anosov diffeomorphisms with partially hyperbolic splitting.
ISSN:2331-8422