91Ó°ÊÓ

Prove that the system of differential equations $$ \dot{x}=x+P(x, y), \quad \dot{y}=y+Q(x, y) $$ where \(P\) and \(Q\) are bounded functions on the entire plane, has at least one equiiibrium position.

Prove that the index of a singular point is independent of the choice of the orientation of the plane.

Find the degree of the mapping of the complex line \(C P^{1}\) onto itself given by a polynomial of degree n.