One-dimensional and two-dimensional dynamics of cubic maps. (30th August 2006)

• Record Type: Journal Article
• Authors: Ilhem, Djellit; Amel, Kara
• Is Part Of: Discrete dynamics in nature and society. Volume 2006(2006)
• Publication Date: 2006-08-30
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/DDNS/2006/15840
• Languages: English
• ISSNs: 1026-0226

Abstract

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.