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On the three-legged accessibility property

Research paper by Raúl Ures, Jana Rodriguez Hertz

Indexed on: 10 May '18Published on: 10 May '18Published in: arXiv - Mathematics - Dynamical Systems



Abstract

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.