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.
HOU, BINGZHE and LUO, LVLIN
"Li--Yorke chaos for invertible mappings on noncompact spaces,"
Turkish Journal of Mathematics: Vol. 40:
2, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/15