Maps with a vanishing denominator. A survey of some results

This paper concerns some results on global dynamical properties and bifurca tions of two-dimensional maps, invertible or noninvertible, presenting a va nishing denominator. This last characteristic may give rise to specific sin gularities of the phase plane, called focal points and prefocal curves. The presence of these sets may cause new types of bifurcations generated by co ntact between them and other singularities, which give rise to new dynamic phenomena and new structures of basin and invariant sets. Some of such beha viors can also be observed in maps without a vanishing denominators, but su ch that some of the inverses have a vanishing denominator.