Resumo:
This dissertation deals with a local bifurcation for planar smooth mappings, depending
on a real parameter, called Neimark-Sacker bifurcation of codimension 1, which, in a
certain sense, shares many similarities with the Hopf bifurcation for ordinary di erential
equations. In both bifurcations, the change in stability of a xed point or equilibrium
point, together with a transversality condition associated with certain eigenvalues of the
Jacobian matrix evaluated at the point, along with one or more nondegeneracy conditions,
allows the appearance or disappearance of an invariant closed curve by the dynamics in the
phase portrait when the parameter is varied. This topic was chosen due to its importance
in the study of discrete dynamical systems and applications in many scienti c areas. In
this sense, the Theorem of Neimark-Sacker Bifurcation of codimension 1 is stated and
proved in the planar case, and applied to the study of two well-known biological models,
namely, the delayed logistic equation and the discrete predator-prey equation.
