Gevrey normal forms for nilpotent contact points of order two

Unique Normal Forms for Nilpotent Planar Vector Fields

Numerical Normal Forms for Codim 2 Bifurcations of Fixed Points with at Most Two Critical Eigenvalues

In this paper we derive explicit formulas for the normal form coefficients to verify the nondegeneracy of eight codimension two bifurcations of fixed points with one or two critical eigenvalues. These include all strong resonances, as well as the degenerate flip and Neimark-Sacker bifurcations. Applying our results to n-dimensional maps, one avoids the computation of the center manifold, but on...

Two Remarks about Nilpotent Operators of Order Two

We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a complex symmetric operator. In fact, we prove that this property characterizes nilpotents of order two among all nonzero bounded operators. Second, we establish...

Gevrey normal forms of pairs of germs of real analytic involutions

Two Normal Forms for Rewriting P Systems