The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy,… (More)
We consider a genus 2 surface, M , of constant negative curvature and we construct a 12-sided fundamental domain, where the sides are segments of the lifts of closed geodesics on M (which determines the Fenchel–Nielsen–Maskit coordinates). Then we study the linear fractional transformations of the side pairing of the fundamental domain. This construction… (More)
It is known as a correspondence between iteration of rational maps and Kleinian groups, and is usually designated as the Sullivan's dictionary. This dictionary enumerates analogies between iteration of holomorphic endomorphisms and action of Kleinian groups. We propose to study explicitly examples establishing the correspondence between the two theories:… (More)
We study the behavior of a unimodal map in two parameters, one of the parameters varies the sign of the Schwarzian derivative the second the value of the maximum. We characterize the behavior of the different dynamics in the parameter space.