Conley barriers and their applications: Chain-recurrence and Lyapunov functions |
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Authors: | Pierre Pageault |
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Institution: | aUMPA, ENS de Lyon, 46 Allée d'Italie, 69007 Lyon, France |
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Abstract: | Given a compact metric space X and a continuous map f from X to itself, we construct a barrier function for chain-recurrence. We use it to endow the space of chain-transitive components with a non-trivial ultrametric distance and to construct Lyapunov functions for f. Most of these constructions are then generalized on an arbitrary separable metric space to a continuous compactum-valued map. |
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Keywords: | Chain-recurrence Lyapunov functions |
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