Mild expansive systems

Time: 14:30 đến 17:00 ngày 17/04/2018, 09:00 đến 11:00 ngày 24/04/2018,

Venue/Location: Thư viện, VIASM

Speaker: Le Huy Tien

Motivated from semi-local dynamics of expansive homeomorphisms, we introduce and study dynamics of the so-called mild expasivity - a genelization of expansivity. It is shown that mild expansivity is different from the known concepts as n-expansivity, countable expansivity, measure expansivity, cw-expansivity. Mild expansive homeomorphisms may have Lyapunov stable points, and exist in compact spaces of any dimension including the unit interval, the unit circle, and the unit sphere. In combining with shadowing property, mild expansivity gives rich implications. In particular, we prove a ”mild” version of the Walter’s theorem on topological stability, and the Spectral Decomposition Theorem. Under generic and $C^1$ -topology context, we
also investigate mild expansivity in connection with hyperbolicity.