N-expansive homeomorphisms with the shadowing property.

We discuss the dynamics of n -expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every n ∈ N , we exhibit an n -expansive homeomorphism, which is not ( n − 1 ) -expansive, has the shadowing property and admits an infinite number of chain-recurrent classes. We discuss some properties of the local stable (unstable) sets of n -expansive homeomorphisms with the shadowing property and use them to prove that some types of the limit shadowing property are present. This deals some direction to the problem of non-existence of topologically mixing n -expansive homeomorphisms that are not expansive. [ABSTRACT FROM AUTHOR]