Dynamics of continued fractions and kneading sequences of unimodal maps

Details Dynamics of continued fractions and kneading sequences of unimodal maps Dynamics of continued fractions and kneading sequences of unimodal maps

2010-12-09

arxiv.org/abs/1012.2131v2

Mathematics

Dynamical Systems

25 pages, 3 figures. New section added with additional results and applications. Figures and references added. Introduction re

Scientific paper

The continued fraction expansion and the binary expansion provide two of the most widely-used methods of description of a real number by means of a sequence of integers. By relating the two codings, we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, and discuss the "exceptional" parameters for these families. By means of this dictionary, one can recover results about the real slice of the Mandelbrot set, and the set of univoque numbers.

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