Li--Yorke chaos for invertible mappings on noncompact spaces

Authors: BINGZHE HOU, LVLIN LUO

Abstract: In this paper, we give two examples to show that an invertible mapping being Li--Yorke chaotic does not imply its inverse being Li--Yorke chaotic, in which one is an invertible bounded linear operator on an infinite dimensional Hilbert space and the other is a homeomorphism on the unit open disk. Moreover, we use the last example to prove that Li--Yorke chaos is not preserved under topological conjugacy.

Keywords: Invertible dynamical systems, Li--Yorke chaos, noncompact spaces, topological conjugacy

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