  In this paper, we give two examples to show that an invertible mapping is
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.
