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Connecting orbits in one-parameter families of flows

Published online by Cambridge University Press:  10 December 2009

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Abstract

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Given a family of flows parametrized by an interval and a Morse decomposition which continues across the interval, a procedure is devised to detect connecting orbits at various parameter values. This is done by putting a small drift on the parameter space and considering the flow on the product of the phase space and the parameter interval. The Conley index and connection matrix are used to analyse the flow on the product space, then the drift is allowed to go to zero to obtain information about the original family of flows. This method can be used to detect connections between rest points of the same index for example.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 359 - 374
Copyright
Copyright © Cambridge University Press 1988

References

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