On specification and measure expansiveness

Abstract

We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Moreover, we find a family of examples with the $N$-expansive property, which are not strong measure expansive. We finally show a spectral decomposition theorem for strong measure expansive dynamical systems with shadowing.

Corrigendum (http://dx.doi.org/10.3934/dcds.2018160) incorporated

References in corpus (4)

• N-expansive homeomorphisms with the shadowing property
• Lipschitz shadowing implies structural stability
• Periodic shadowing and $\Omega$-stability
• Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity

Cited by in corpus (6)

• Beyond topological hyperbolicity: the L-shadowing property
• Positively n-expansive homeomorphisms and the L-shadowing property
• Continuum-wise hyperbolicity
• Countably and entropy expansive homeomorphisms with the shadowing property
• First-time sensitive homeomorphisms
• Continuum-wise expansive Non-Autonomous Discrete Systems