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Attractors for maps with fractional inverse. (English) Zbl 1137.37021

The paper presents some dynamical properties and specific contact bifurcations of two-dimensional maps having an inverse with vanishing denominator. The notions of focal point and prefocal curve are introduced and their role in the geometric properties of a rational map is described. The link existing between basin bifurcation of a map with fractional inverse and the prefocal curve of this inverse is studied. Results obtained in the paper are illustrated by considering the Bogdanov map.

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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