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Bull. Korean Math. Soc. 2014; 51(2): 387-400

Printed March 1, 2014

https://doi.org/10.4134/BKMS.2014.51.2.387

Copyright © The Korean Mathematical Society.

Spectral decomposition of $k$-type nonwandering sets for ${\mathbb Z}^2$-actions

Daejung Kim and Seunghee Lee

Chungnam National University, Chungnam National University

Abstract

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We prove that the set of $k$-type nonwandering points of a ${\mathbb Z}^2$-action $T$ can be decomposed into a disjoint union of closed and $T$-invariant sets $B_1, \ldots ,B_l$ such that $T|_{B_i}$ is topologically $k$-type transitive for each $i=1,2, \ldots,l$, if $T$ is expansive and has the shadowing property.

Keywords: spectral decomposition theorem, $k$-type nonwandering sets, expansive, shadowing property

MSC numbers: 37B10, 37C85, 54H20

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