Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 343-355

Attractors for maps with fractional inverse

M. R. Ferchichi and I. Djellit

Department of Mathematics, Faculty of Sciences, University of Annaba, BP 12, Annaba 23000, Algeria

Received 5 November 2004

Copyright © 2005 M. R. Ferchichi and I. Djellit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.