Geometric constructions and multifractal analysis for boundary hyperbolic maps

MESON, ALEJANDRO M.; VERICAT FERNANDO

DYNAMICAL SYSTEMS

TAYLOR & FRANCIS LTD

Lugar: [Londres]; Año: 2002 vol. 17 p. 203 - 213

1468-9367

In this paper we present geometric constructions based on the method by Series for coding geodesics in the hyperbolic disc. For this are used certain special types of one-dimensional maps defined on the boundary of the hyperbolic plane. These types of maps do not require additional assumptions to ensure the existence of Gibbs states. We connect geometrical constructions from limit sets of Fuchsian groups with multifractal analysisby modifying the definition of a local entropy by Takens and Verbitski.