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arXiv · 1004.3410

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

Stefan Liebscher
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Abstract

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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Stefan Liebscher. 2010-09-07. Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters. https://arxiv.org/abs/1004.3410

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