[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j190453

EXPANDING MEASURES FOR HOMEOMORPHISMS WITH EVENTUALLY SHADOWING PROPERTY

Dong, Meihua (Department of Mathematics College of Science Yanbian University)
Lee, Keonhee (Department of Mathematics Chungnam National University)
Nguyen, Ngocthach (Department of Mathematics Chungnam National University)

Publication Information

Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 935-955 More about this Journal

Abstract

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

Keywords

expanding measures; eventually shadowing property; ${\Omega}$ -stability; spectral decomposition;

Citations & Related Records

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