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Global Dynamics Beyond Hyperbolicity
[2017 KAIST Math. Colloquium]
Date: 2017-11-09
Speaker : 이건희 (충남대학교)
Abstract : Hyperbolic dynamical systems are nowadays fairly well understood from the topological and ergodic point of view. In this talk, we discuss some recent and ongoing works on the dynamics beyond hyperbolicity. In the first part, we will provide a characterization of robustly shadowable chain transitive sets for C1-vector fields on compact smooth manifolds. In the second part, we extend the concepts of topological stability and pseudo-orbit tracing property from homeomorphisms to Borel measures, and prove that every expansive measure with the pseudo-orbit tracing property is topologically stable. This represents a measurable version of the stability theorem by Peter Walters. The first part is joint work with M. Reza, and the second part is joint work with C.A. Morales.
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