Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 15840, 13 pages

One-dimensional and two-dimensional dynamics of cubic maps

Djellit Ilhem1 and Kara Amel2

1Department of Mathematics, University of Annaba, Annaba BP 12 23000, Algeria
2Department of Physics, University of Sétif, Sétif 19000, Algeria

Received 20 December 2005; Accepted 24 March 2006

Copyright © 2006 Djellit Ilhem and Kara Amel. 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.


We concentrate on the dynamics of one-dimensional and two-dimensional cubic maps, it describes how complex behaviors can possibly arise as a system parameter changes. This is a large class of diffeomorphisms which provide a good starting point for understanding polynomial diffeomorphisms with constant Jacobian and equivalent to a composition of generalized Hénon maps. Due to the theoretical and practical difficulties involved in the study, computers will presumably play a role in such efforts.