Plane maps with denominator I: some generic properties

GI Bischi, L Gardini, C Mira - International Journal of bifurcation and …, 1999 - World Scientific
International Journal of bifurcation and Chaos, 1999World Scientific
This paper is devoted to the study of some global dynamical properties and bifurcations of
two-dimensional maps related to the presence, in the map or in one of its inverses, of a
vanishing denominator. The new concepts of focal points and of prefocal curves are
introduced in order to characterize some new kinds of contact bifurcations specific to maps
with denominator. The occurrence of such bifurcations gives rise to new dynamic
phenomena, and new structures of basin boundaries and invariant sets, whose presence …
This paper is devoted to the study of some global dynamical properties and bifurcations of two-dimensional maps related to the presence, in the map or in one of its inverses, of a vanishing denominator. The new concepts of focal points and of prefocal curves are introduced in order to characterize some new kinds of contact bifurcations specific to maps with denominator. The occurrence of such bifurcations gives rise to new dynamic phenomena, and new structures of basin boundaries and invariant sets, whose presence can only be observed if a map (or some of its inverses) has a vanishing denominator.
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