Geodesic
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Electronic journal of differential equations, Tome 2011 (2011)
Zbl   arXiv
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 
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/
@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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