Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Dynamical Systems
2012-07-12 v2
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.
Keywords
Cite
@article{arxiv.1004.3410,
title = {Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters},
author = {Stefan Liebscher},
journal= {arXiv preprint arXiv:1004.3410},
year = {2012}
}
Comments
corrected typos, minor clarifications in the formulation of the main theorem