A Unified Renormalization Scheme for Two-Piecewise Monotonous Maps of the Interval
In this paper we study the relation between symbolic dynamics and renormalization of maps from the interval to itself, with one discontinuity and two branches of continuity and monotonicity. We introduce a symbolic formalism based on kneading theory that permits us to deal, in a unified way, with the four cases that can occur, at the same time. Using this formalism we also study properties of similarity from the four spaces of kneading invariants.