The specification property on a set-valued map and its inverse limit

Abstract

In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and prove some elementary results of these properties. We end with a few results regarding invariant measures for set-valued functions and their associated inverse limits.

Cited by in corpus (5)

• Topological entropy of closed sets in $[0,1{]}^2$
• Devaney Chaos on a Set-valued Map and Its Inverse Limit
• Transitivity and Mixing Properties of Set-Valued Dynamical Systems
• Periodicity and Indecomposability in Generalized Inverse Limits
• Expansiveness, Lyapunov exponents and entropy for set valued maps