Geodesic
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 34C23, 34C20, 58K05
Keywords: manifolds of equilibria, bifurcation without parameters, singularities of vector fields 
@article{EJDE_2011__2011__a78,
     author = {Liebscher,  Stefan},
     title = {Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1364.34069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a78/}
}
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AU  - Liebscher,  Stefan
TI  - Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
JO  - Electronic journal of differential equations
PY  - 2011
VL  - 2011
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LA  - en
ID  - EJDE_2011__2011__a78
ER  - 
%0 Journal Article
%A Liebscher,  Stefan
%T Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
%J Electronic journal of differential equations
%D 2011
%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a78/
%G en
%F EJDE_2011__2011__a78
Liebscher,  Stefan. Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a78/