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.


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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