Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 1, Pages 69-85
doi:10.1155/DDNS.2005.69

Irreducible complexity of iterated symmetric bimodal maps

J. P. Lampreia,1 R. Severino,2 and J. Sousa Ramos3

1Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisboa, Portugal
2Departamento de Matemática, Universidade do Minho, Braga 4710-057, Portugal
3Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, Portugal

Received 9 March 2004

Copyright © 2005 J. P. Lampreia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.