Nilpotent Systems Admitting an Algebraic Inverse Integrating Factor over $${{\mathbb{C}}((x,y))}$$

A survey on the inverse integrating factor . ∗

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relation with limit cycles and their bifurcations. This paper is a summary of all the res...

On meromorphic mappings admitting an Algebraic Addition Theorem

A proper or singular abelian mapping from C to C n is parametrized by n meromorphic functions with at most 2n periods. We develop the existence and structure theorems of the classical theory of an abelian mapping purely on the basis of its defining functional equation, the so-called algebraic addition theorem (AAT), with no appeal to any representation as quotients of theta functions. We offer ...

Algebraic proof systems over formulas

Dynamical Systems Admitting Normal

Let S be a hypersurface in Riemannian manifold M . One of the ways for deforming S consists in shifting points, which constitute S, along trajectories of some Newtonian dynamical system. Such situation arises in describing the propagation of electromagnetic wave (light) in non-homogeneous media in the limit of geometric optics. Hypersurface S models wave front set (the set of points with consta...

Self–Dual Algebraic Varieties and Nilpotent Orbits

We give a construction of nonsmooth self-dual projective algebraic varieties. They appear as certain projectivized orbit closures for some linear actions of reductive algebraic groups. Applying this construction to adjoint representations, we obtain geometric characterization of distinguished nilpotent elements of semisimple Lie algebras [BC1], [BC2] (i.e., nilpotent elements whose centralizer ...