Dynamics on Hyperspaces
Abstract
Given a compact metric space (X; ) and a continuous function f:X→ X, we study the dynamics of the induced map f on the hyperspace of the compact subsets of X. We show how the chain recurrent set of f and its components are related with the one of the induced map. The main result of the paper proves that, under mild conditions, the numbers of chain components of f is greater than the ones of f. Showing the richness in the dynamics of f which cannot be perceived by f.
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