Resumen de Applications of the Euler characteristic in bifurcation theory

Slawomir Rybicki

• Let f: Rn x Rn ? Rn be a continuous map such that f(0,?) = 0 for all ? Î Rk. In this article we formulate, in terms of the Euler characteristic of algebraic sets, sufficient conditions for the existence of bifurcation points of the equation f(x,?) = 0. Moreover we apply these results in bifurcation theory to ordinary differential equations. It is worth to point out that in the last paragraph we show how to verify, by computer, the assumptions of the theorems of this paper.