Topological entropy of monotone maps and confluent maps on regular curves. (English) Zbl 1093.54013
Let \(f\) be a confluent map on a regular curve such that the number of components of \(f^{-1}(y)\) is uniformly bounded by \(k\). Then, the topological entropy \(h(f) \leq \log k\). As a corollary the autor shows that the topological entropy of any monotone map of any regular curve is zero.
Reviewer: Jerzy Ombach (Kraków)
MSC:
54H20 | Topological dynamics (MSC2010) |
54C70 | Entropy in general topology |
37E25 | Dynamical systems involving maps of trees and graphs |
37B40 | Topological entropy |