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SPECTRAL DECOMPOSITION OF k-TYPE NONWANDERING SETS FOR ℤ2-ACTIONS

Kim, Daejung;Lee, Seunghee

  • Received : 2012.06.21
  • Published : 2014.03.31

Abstract

We prove that the set of k-type nonwandering points of a Z2-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

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