Defines (i,j)-shadowing for closed relations on compact spaces and gives characterizations for finite-branching, diagonal-containing, and isometry-related relations.
The specification property on a set-valued map and its inverse limit
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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.
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Shadowing in CR-Dynamical Systems
Defines (i,j)-shadowing for closed relations on compact spaces and gives characterizations for finite-branching, diagonal-containing, and isometry-related relations.