Positively n-expansive homeomorphisms and the L-shadowing property

Abstract

We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in [7]. The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.

13 pages

References in corpus (3)

• N-expansive homeomorphisms with the shadowing property
• On specification and measure expansiveness
• Shadowing, asymptotic shadowing and s-limit shadowing

Cited by in corpus (5)

• Beyond topological hyperbolicity: the L-shadowing property
• Continuum-wise hyperbolicity
• Countably and entropy expansive homeomorphisms with the shadowing property
• Suspensions of homeomorphisms with the two-sided limit shadowing property
• Sensitivity, local stable/unstable sets and shadowing