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One-dimensional and two-dimensional dynamics of cubic maps

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 Henon maps. Due to the theoretical and practical difficulties involved in the study, computers will presumably play a role in such efforts.