Computer Algebra of Vector Bundles
and Complex Foliations of Polynomial Dynamical Systems

Nikolaj M. Glazunov

Glushkov Institute of Cybernetics NAS
252650 Ukraine Kiev GSP-650 Glushkov prospekt 40
Email: glanm@d105.icyb.kiev.ua

Abstract

We investigate global and some local properties of (complex) polynomial dynamical systems (DS). Let M is a compact invariant manifold of DS. Investigation of DS under the presence of M (which defines a complex analytic foliation with singularities) leads to the introduction of algebraic geometric invariants: blow-ups and their divisors, fiber bundles, indexes of self-intersection, characteristic classes of vector bundles, and to some another.
Algebraic methods of their computation will be considered.
Applications to existence of separatrixes of foliations and first integrals and to problems of local and global stability will be done.