Dinâmica de aplicações quadráticas conservativas do plano

Abstract

In this work will be characterized the generic form of plane quadratic applications that preserve area, orientation and that have a fixed point.It will evaluate the linear stability of fixed points, detecting the conditions to hyperbolicity and ellipticity.Also, will be studied the behavior of the first Birkhoff coefficient in the elliptical case not resonant and its dynamical consequences, as the existence of invariants closed curves. The dynamics in the hyperbolic case will be described, showing the intersection of stable andunstable manifolds as well the existence of a compact that have a not trivial dynamics.