Free University Berlin, Institute of Mathematics
Arnimallee 3, D-14195 Berlin, Germany
email: stefan.liebscher@fu-berlin.de
http://dynamics.mi.fu-berlin.de
Stefan Liebscher
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.
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Stefan Liebscher Free University Berlin, Institute of Mathematics Arnimallee 3, D-14195 Berlin, Germany email: stefan.liebscher@fu-berlin.de http://dynamics.mi.fu-berlin.de |
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