Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 343-355
Attractors for maps with fractional inverse
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.