Irreducible complexity of iterated symmetric bimodal maps

Details Irreducible complexity of iterated symmetric bimodal maps Irreducible complexity of iterated symmetric bimodal maps

2004-03-08

arxiv.org/abs/math/0403118v1

Mathematics

Dynamical Systems

Scientific paper

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 $\ast $-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.

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