ABSTRACT
The bifurcation set separates regions of parameter space characterized by inequivalent dynamics. The simplest cases of bifurcations are associated with the study of the number and stability of fixed points in flows and maps (periodic orbits). These types of orbit are localized in phase space and their transformations, with respect to changes of parameters, can be studied restricting the analysis to a small neighbourhood (in phase space) of the fixed point. In partial opposition to local bifurcations are global bifurcations, in this case the analysis cannot be restricted to a small region of phase space and requires some knowledge of the dynamics in an extended region. The saddle-node bifurcation for maps occurs when the linearized map at the fixed point presents one (and only one) eigenvalue equal to one. In most respects, the saddle-node bifurcation for maps (or periodic orbits) does not differ from the saddle-node in flows.
