Contact Bifurcations in
Two-Dimensional Endomorphisms Related with Homoclinic or
Heteroclinic Orbits
M.R. Ferchichi
1, I.Djellit
2, J.C. Sprott
3
1,2Laboratoire Math´ematiques, Dynamique et
Mod´elisation, University of Annaba - Faculty of Sciences,
Department of
Mathematics - P.B.12- 23000 Annaba , Algeria
3University of Wisconsin, Department of Physics -
Madison, WI 53706 USA
(Received 9 June 2010, accepted
30 August 2010)
ABSTRACT
In this paper we show the homoclinic bifurcations which are
involved in some contact bifurcations of basins of attraction in
noninvertible two-dimensional map. That is, we are interested in
the link between contact bifurcations of a chaotic area and
homoclinic bifurcations of a saddle point or of an expanding fixed
point located on the boundary of the basin of attraction of the
chaotic area. We shall analyze the particular
case of a map having up to three distinct preimages, and the
basins’s bifurcations are investigated by use of the technique
of critical curves.
Ref: M. R. Ferchichi, I. Djellit, and