Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters

Details Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters

2010-04-20

arxiv.org/abs/1004.3410v2

Mathematics

Dynamical Systems

corrected typos, minor clarifications in the formulation of the main theorem

Scientific paper

We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. In the present paper we provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.

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