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Irreducible complexity of iterated symmetric bimodal maps

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  • J. P. Lampreia
  • R. Severino
  • J. Sousa Ramos

Abstract

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a ∗ -product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the ∗ -product induced on the associated Markov shifts.

Suggested Citation

  • J. P. Lampreia & R. Severino & J. Sousa Ramos, 2005. "Irreducible complexity of iterated symmetric bimodal maps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2005, pages 1-17, January.
    • Handle: RePEc:hin:jnddns:525740
    DOI: 10.1155/DDNS.2005.69
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