Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 343-355
doi:10.1155/DDNS.2005.343

Attractors for maps with fractional inverse

Abstract

In this work, we consider some dynamical properties and specific contact bifurcations of two-dimensional maps having an inverse with vanishing denominator. We introduce new concepts and notions of focal points and prefocal curves which may cause and generate new dynamic phenomena. We put in evidence a link existing between basin bifurcation of a map with fractional inverse and the prefocal curve of this inverse.