Examples of codimension

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One would not expect to observe the more degenerate (higher codimension) singularities like transcritical bifurcations.
Indeed, given (4.8) then we see that we have (4.9) unless some relations-a linear manifold of positive codimension-holds among the coefficients.
We want to give an interpretation of this as an average asymptotic linking number of a suitable vector field and a measured codimension-two foliation.
Let us now describe the construction of a return map on a codimension-one surface of section.
The half-spaces, of - which it is the intersection, are determined by codimension-one subspaces orthogonal to the edges connecting vi to neighboring vertices.
Such paths of singularities may in turn have singularities at more degenerate (higher codimension) singularities.
These are proved to be the only codimension-one bifurcations.
This property is shared by the unfoldings of finite codimension parabolic germs.
The behaviour as the system parameters are varied slightly away from the codimension-n point can be investigated using the normal forms (universal unfolding).
Surfaces intersect the sphere in curves, which meet in points corresponding to curves of codimension-two bifurcations in the bifurcation set.
The rotating double-diffusive system is consequently expected to show a line of codimension-two points that accumulate at a codimension-three point (a tertiary bifurcation).
The idea is to consider the full 'ensemble' (family of graphics), including the bordering graphic(s) which may or may not have higher codimension.
Roughly speaking, they obtain topological results about certain manifolds provided they admit special codimension 1 immersions.
This work points in the direction of trying to get a global picture of all the codimension two bifurcations for diffeomorphisms.
In this article, we classify the germs of holomorphic singular simple foliations of codimension 1 and dimension n 3, in the resonant case.

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