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On gradient dynamical system on semi-Riemannian manifolds

✍ Scribed by Jens Chr. Larsen

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
805 KB
Volume
6
Category
Article
ISSN
0393-0440

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✦ Synopsis

We considergradient dynamical systems on a serni-Riemannian manifold of arbitrary index. The main point of the paper is the introduction of the concepts causality subsets, causality function and sector stability. As a main application we provide conditions assuring, that the non wandering points areprecisely the singular points of the gradient field. Fwlhermore we show, that every nonconstant recurrent orbit for thegradient fleidmust intersect one of the causality subsets and that the stable and unstable manifolds belonging to a hyperbolic singularpoint for the gradient fIeld are orthogonal.

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