ITERATION OF DIFFERENTIABLE FUNCTIONS UNDER m-MODAL MAPS

• Author(s): Correia, Maria de Fátima ; Ramos, Carlos ; Vinagre, Sandra
• Date: 2011
• Persistent ID: http://hdl.handle.net/10174/3796
• Origin: Repositório Científico da Universidade de Évora
• Subject(s): symbolic dynamics; infinite dimensional dynamical systems; m-modal maps; iteration theory
• Document Type: Article
• Language: English

Description

We consider the dynamical system (A,T), where A is a class of differentiable real functions defined on some interval and T:A→A is an operator Tφ:= foφ, where f is a function on the real line. In this work we introduce and develop some techniques of symbolic dynamics for the dynamical system (A,T). We analyze in detail the case in which T arises from a differentiable m-modal map f. In this case we obtain a combinatorial description of the orbits of (A,T) which depends on the combinatorial description of the orbits of one dimensional dynamical system induced by f on the interval.