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Conley index. (English) Zbl 1035.37010
Fiedler, Bernold (ed.), Handbook of dynamical systems. Volume 2. Amsterdam: Elsevier (ISBN 0-444-50168-1/hbk). 393-460 (2002).
This expository text presents basic facts concerning the Conley index theory, both in continuous and discrete time settings. Except of the basic definitions and results, the topics considered in the text include attractor-repeller pairs, Morse decompositions, connection and transition matrices, the existence of periodic orbits, symbolic dynamics, singular perturbation theory, and the multivalued Conley index together with its relations to computer-assisted proofs. All topics are illustrated by natural examples.
For the entire collection see [Zbl 0982.37002].

MSC:
37B30 Index theory for dynamical systems, Morse-Conley indices
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
34E15 Singular perturbations for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37B35 Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
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