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Zbl 1091.37006
Srzednicki, Roman
Ważewski method and Conley index. (English)
[A] Cañada, A. (ed.) et al., Ordinary differential equations. Vol. I. Amsterdam: Elsevier/North Holland. Handbook of Differential Equations, 591-684 (2004). ISBN 0-444-51128-8/hbk

The author gives a survey on topological methods in dynamical systems based on the Ważewski retract theorem. He provides a historical context as well as the current exposition of the method with applications to ordinary differential equations and inclusions and for retarded functional-differential equations. He proves many interesting properties of isolating blocks concerning their homological properties and connections with the Ljusternik-Schnirelmann theory. A variant of the Ważewski set, namely isolating segments, is used for detecting periodic solutions and chaos in nonautonomous periodic in time ODEs. The paper is finished by a chapter about isolated invariant sets and the Conley index.
[Klaudiusz Wójcik (Kraków)]

MSC 2000:: *37B30 Index theory, Morse-Conley indices
34A34 Nonlinear ODE and systems, general
34A60 ODE with multivalued right-hand sides
34K99 Functional-differential equations
34B15 Nonlinear boundary value problems of ODE
55M30 Lyusternik-Shnirel'man category of a space

Keywords: Conley index; Ważewski set; Ljusternik-Schnirelmann category; isolating block; isolating segment

Cited in: Zbl 1192.45002

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