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Mappings and homological properties in the Conley index theory

Published online by Cambridge University Press:  10 December 2009

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Abstract

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The role in the Conley index of mappings between flows is considered. A class of maps is introduced which induce maps on the index level. With the addition of such maps to the theory, the homology Conley index becomes a homology theory. Using this structure, an analogue of the Lefschetz theorem is proved for the Conley index. This gives a new condition for detecting fixed points of flows, extending the classical Euler characteristic condition.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 175 - 198
Copyright
Copyright © Cambridge University Press 1988

References

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