Title    name
2017 KAIST Math. Colloquium
 
  Title
  Speaker 이건희
  Date 2017-11-09
  Host
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.   
 
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.