Robustly measure expansiveness for C1 vector fields

Published in: Quaestiones Mathematicae
Volume 43, issue 4, 2020 , pages: 569–582
DOI: 10.2989/16073606.2019.1584594
Author(s): Manseob LeeDepartment of Mathematics, Korea


Let X be a C1 vector field of a compact connected boundaryless smooth smooth Riemannian manifold M with dimM ≥ 3. We show the following: (i) if the chain recurrence set ????(X) is robustly measure expansive, then it is Axiom A without cycles; and (ii) if the homoclinic class H(Orb(p), X) that contains a hyperbolic periodic orbit Orb(p) is generic-robustly measure expansive, then it is hyperbolic.

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