41 research outputs found
Irreducible complexity of iterated symmetric bimodal maps
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
Ä-product of Markov matrices.
In this paper we introduce a Ä-operation over Markov transition matrices, in the context of subshift of finite type, reproducing symbolic properties of the iterates of the critical point on a one-parameter family of unimodal maps. To the *-product between kneading sequences we associate a Ä-product between the corresponding Markov matrices