IJPAM: Volume 70, No. 2 (2011)

ITERATION OF DIFFERENTIABLE FUNCTIONS
UNDER $m$-MODAL MAPS

Maria de Fátima Correia$^1$, Carlos C. Ramos$^2$, Sandra M. Vinagre$^3$
Department of Mathematics
University of Evora
Rua Romao Ramalho, 59, Evora, 7000-671, PORTUGAL


Abstract. We consider the dynamical system $(\mathcal{A}, T)$, where $\mathcal{A}$ is a class of differentiable real functions defined on some interval and $T:\mathcal{A}\rightarrow \mathcal{A}$ is an operator $T\phi:= f\circ \phi$, 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 $(\mathcal{A}, T)$. 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 $(\mathcal{A}, T)$ which depends on the combinatorial description of the orbits of one dimensional dynamical system induced by $f$ on the interval.

Received: February 10, 2011

AMS Subject Classification: 37B10, 39B12, 37C05, 26A18

Key Words and Phrases: symbolic dynamics, infinite dimensional dynamical systems, $m$-modal maps, iteration theory

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 2