Discrete Dynamics in Nature and Society
Volume 2006 (2006), Issue 5, Article ID 15840, 13 pages
doi:10.1155/DDNS/2006/15840
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
Abstract
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.