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

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.