Trees with snowflakes and zero entropy maps
A one-dimensional connected and contractible branching manifold with finitely many branching points is called a tree, and a finite union of trees is called a forest. The main result of the paper is theorem 3, which gives necessary and sufficient conditions that a continuous self- mapping of a forest has zero entropy. This generalizes the corresponding statement for maps of the interval based on Sharkovskij's theorem [\textit{A. N. Sharkovskij}, Ukr. Mat. J. 16, 61-71 (1964; Zbl 0122.175)] on the structure of periodic points and on Misiurewicz's theorem [\textit{M. Misiurewicz}, Bull. Pol. Acad. Sci., Sér. Sci. Math. 27, 167-169 (1979; Zbl 0423.54032)] on the existence of horseshoes for positive entropy maps.
scientific article; zbMATH DE number 590282