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Plane maps with denominator. I: Some generic properties. (English) Zbl 0996.37052

The authors study some generic properties of two-dimensional fractional rational maps that are not defined in the whole plane, due to the presence, in at least one component of the map, of a denominator that can vanish. They introduce the new concepts of focal point and prefocal curve in order to characterize the particular geometric and dynamic properties, together with some new kinds of bifurcations, for a class of map mentioned above.

MSC:

37E99 Low-dimensional dynamical systems
37G10 Bifurcations of singular points in dynamical systems
37C20 Generic properties, structural stability of dynamical systems
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