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Morse equations and unstable manifolds of isolated invariant sets

Rodríguez Sanjurjo, José Manuel (2003) Morse equations and unstable manifolds of isolated invariant sets. Nonlinearity, 16 (4). pp. 1435-1448. ISSN 0951-7715

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Abstract

We describe a new way of obtaining the Morse equations of a Morse decomposition of an isolated invariant set. This is achieved through a filtration of truncated unstable manifolds associated with the decomposition. The results in the paper make it possible to calculate the Morse equations (and also the Conley index) in many interesting situations without using index pairs. We also study the intrinsic topology of the unstable manifold and obtain new duality properties of the cohomological Conley index.

Item Type:Article
Uncontrolled Keywords:Index theory, Morse-Conley indices; Strange attractors, chaotic dynamics; Stability theory
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16824
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Last Modified:07 Feb 2014 09:36

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