ON PERIODIC-ORBITS OF TRAPEZOID MAPS

Iterations of a special one-dimensional map (trapezoid map) which is a piecewise linear map with a flat top are studied. Using a symbolic dynamical method, it is shown that the stable periodic orbits of the map are characterized as finite shift maximal sequences in the sense extended by Sun and Helmberg and the parameter regions where the map produces a stable periodic orbit with any period are determined. The method used in the present paper is a simple method which converts a bifurcation problem of trapezoid maps to an initial value problem of a tent (triangle) map. This method is applicable to various chaotic maps which have a flat segment. © 1993 Academic Press, Inc.