Topological entropy of maps on regular curves
It is known that the topological entropy of a homeomorphism on a regular curve is zero, see \textit{G. T. Seidler} [Proc. Am. Math. Soc. 108, No.~4, 1025--1030 (1990; Zbl 0703.54021)]. Here, more generally, the topological entropy of a map \(f\) on a regular curve \(X\) is studied in terms of the growth of the number of components of \(f^{-n}(y), y\in X\). The proof of the main statement uses the boundary bumping theorem from [\textit{S. B. Nadler jun.}, Continuum theory. An introduction, Pure and Applied Mathematics (New York, Marcel Dekker), 158, New York: Marcel (1992; Zbl 0757.54009)].
scientific article; zbMATH DE number 5132965
scientific article