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One-dimensional and two-dimensional dynamics of cubic maps

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  • Djellit Ilhem
  • Kara Amel

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.

Suggested Citation

  • Djellit Ilhem & Kara Amel, 2006. "One-dimensional and two-dimensional dynamics of cubic maps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-13, August.
    • Handle: RePEc:hin:jnddns:015840
    DOI: 10.1155/DDNS/2006/15840
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    Cited by:

    1. da Costa, Diogo Ricardo & Hansen, Matheus & Batista, Antonio Marcos, 2019. "Parametric perturbation in a model that describes the neuronal membrane potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 519-525.

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