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Bifurcations in symplectic space

G. Ishikawa, S. Janeczko (2008)

Banach Center Publications

In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.

Invariants of equidimensional maps

Joachim H. Rieger (2003)

Banach Center Publications

To a given complex-analytic equidimensional corank-1 germ f, one can associate a set of integer 𝓐-invariants such that f is 𝓐-finite if and only if all these invariants are finite. An analogous result holds for corank-1 germs for which the source dimension is smaller than the target dimension.

Real deformations and invariants of map-germs

J. H. Rieger, M. A. S. Ruas, R. Wik Atique (2008)

Banach Center Publications

A stable deformation f t of a real map-germ f : , 0 p , 0 is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification f t are real. A related notion is that of a good real perturbation f t of f (studied e.g. by Mond and his coworkers) for which the homology of the image (for n < p) or discriminant (for n ≥ p) of f t coincides with that of f C t . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good real perturbation....

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