Quasi Periodicity in Local Bifurcation Theory

摘要

The paper presents an overview of some results obtained recently in the local theory of bifurcations of dynamical systems, which are concerned with quasi periodic flow. With this 'local theory' we here mean the qualitative (topological) behavior of parametrized systems of ordinary differential equations near equilibrium points, especially the changes in this behavior as the parameters move. The results of this paper involve some techniques, connected with so called small divisors which come from the Kolmogorov-Arnold-Moser theory into this field of bifurcations. Although these techniques found their origin in Hamiltonian dynamics (celestial mechanics, stability of the solar system), it is by now well known that their scope of applicability is much wider.