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Linearization of vector fields on the orbit space of the action of a compact Lie group

Published online by Cambridge University Press:  01 May 1997

MURIEL KŒNIG
MURIEL KŒNIG
Affiliation:
Institut Non Linéaire de Nice, UMR CNRS-UNSA 129, 1361 route des Lucioles, 06560 Valbonne, France
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Abstract

In this paper we present results which relate the linearization of a G-equivariant vector field at an equilibrium to the linearization of the vector field obtained by projection on the orbit space of the group action. This allows us to propose a notion of hyperbolicity for an equilibrium of the projected vector field which is compatible with the orbit space structure. It provides an alternative to the notion of normal hyperbolicity for relative equilibria (flow invariant group orbits) developed by Field [9, 10].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 3 , May 1997 , pp. 401 - 424
Copyright
Cambridge Philosophical Society 1997

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