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Shadowing property for set-valued map and its inverse limit
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In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics, then certain induced inverse limit systems have the shadowing property. Additionally, we prove that a continuous set-valued map has the shadowing property if and only if some of its induced inverse limit system also has shadowing property. Finally, we establish that the shadowing property of a set-valued map is equivalent to the shadowing property of its induced inverse set-valued system.
Forward citations
Cited by 2 Pith papers
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Shadowing property and transitivity of a set-valued map and its inverse limit
Shadowing of F, shadowing of F←, and shadowing of the shift maps on lim←F and lim←F← are equivalent for surjective u.s.c. set-valued maps on compact metric spaces.
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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.
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