Dynamics of continued fractions and kneading sequences of unimodal maps
arXiv preprint arXiv:1012.2131, 2010•arxiv.org
In this paper we construct a correspondence between the parameter spaces of two families
of one-dimensional dynamical systems, the alpha-continued fraction transformations
T_alpha and unimodal maps. This correspondence identifies bifurcation parameters in the
two families, and allows one to transfer topological and metric properties from one setting to
the other. As an application, we recover results about the real slice of the Mandelbrot set,
and the set of univoque numbers.
of one-dimensional dynamical systems, the alpha-continued fraction transformations
T_alpha and unimodal maps. This correspondence identifies bifurcation parameters in the
two families, and allows one to transfer topological and metric properties from one setting to
the other. As an application, we recover results about the real slice of the Mandelbrot set,
and the set of univoque numbers.
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the alpha-continued fraction transformations T_alpha and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results about the real slice of the Mandelbrot set, and the set of univoque numbers.
arxiv.org