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Conley barriers and their applications: Chain-recurrence and Lyapunov functions

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
156
Issue
15
Identifiers
DOI: 10.1016/j.topol.2009.06.013
Keywords
  • Chain-Recurrence
  • Lyapunov Functions

Abstract

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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