Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 63, pp. 1-12.

Title: Dynamics near manifolds of equilibria of codimension one
       and bifurcation without parameters
       
Author: Stefan Liebscher (Free Univ. Berlin, Germany)

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. 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.

Submitted April 10, 2010. Published May 17, 2011.
Math Subject Classifications: 34C23, 34C20, 58K05.
Key Words: Manifolds of equilibria; bifurcation without parameters; 
           singularities of vector fields.