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FIELD Math:Topology
DATE May 22 (Wed), 2019
TIME 16:00-17:00
PLACE 1423
SPEAKER 이건희
HOST Kim, Inkang
INSTITUTE 충남대학교
TITLE Spectral Decomposition and $\Omega$-Stability of Flows \\ with Expansive Measures
ABSTRACT

We discuss some recent and ongoing works on the dynamics of flows with various expansive measures.
In particular, we present a measurable version of the Smale's spectral decomposition theorem for flows. More precisely, we prove that if a flow $\phi$ on a compact metric space $X$ is invariantly measure expanding on its chain recurrent set $CR(\phi)$ and has the invariantly measure shadowing property on $CR(\phi)$ then $\phi$ has the spectral decomposition, i.e. the nonwandering set $\Omega(\phi)$ is decomposed by a disjoint union of finitely many invariant and closed sets on which $\phi$ is topologically transitive. Moreover we show that if $\phi$ is invariantly measure expanding on $CR(\phi)$ then it is invariantly measure expanding on $X$. Using this, we characterize the measure expanding flows on a compact $C^{\infty}$ manifold via the notion of $\Omega$-stability.
{\it This is joint work with N. Nguyen.}

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