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Chain transitivity, attractivity, and strong repellors for semidynamical systems. (English) Zbl 1129.37306
Summary: Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, and permanence. A result of Schreiber on robust permanence is improved.

37B35 Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
37B25 Stability of topological dynamical systems
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
54H20 Topological dynamics (MSC2010)
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