Abstract
The aim of this paper is to present a structure result on the infinite -limit sets of continuous triangular mappings defined on the unit square, i.e. maps of the form (x, y)(f(x), g(x, y)) having zero topological entropy in the base map f and on the fibres defined over the periodic points of f. We show for this class of systems that the infinite -limit sets of the points of the form (x, y), where x is a periodic point of f, have a solenoidal distribution. It extends the results by Smital [J. Smital, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), pp. 269-282] on zero topological entropy of continuous interval maps. An application is presented.