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ON THE STRUCTURE OF THE KNEADING SPACE OF BIMODAL DEGREE ONE CIRCLE MAPS

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Spain

and

Departamento de Ciencias, Físicas, Matemáticas y de la Computación, Universidad CEU Cardenal Herrera, San Bartolome 55, 46115 Alfara del Patriarca, Valencia, Spain

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https://doi.org/10.1142/S0218127410027301Cited by:0 (Source: Crossref)

Abstract

In this paper, we introduce an index space and two ⋆-like operators that can be used to describe bifurcations for parametrized families of degree one circle maps. Using these topological tools, we give a description of the kneading space, that is, the set of all dynamical combinatorial types for the class of all bimodal degree one circle maps considered as dynamical systems.

Dedicated to the memory of Valery S. Melnik

Keywords:

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