In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the α-continued fraction transformations Tα 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.
Dynamics of continued fractions and kneading sequences of unimodal maps / Bonanno, C.; Carminati, C.; Isola, S.; Tiozzo, G.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 33:4(2013), pp. 1313-1332. [10.3934/dcds.2013.33.1313]
Dynamics of continued fractions and kneading sequences of unimodal maps
Tiozzo G.
2013
Abstract
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the α-continued fraction transformations Tα 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
