Bobok, Jozef On entropy of patterns given by interval maps. (English) Zbl 0938.54037 Fundam. Math. 162, No. 1, 1-36 (1999). The topological entropy of patterns given by continuous interval maps is studied. It is shown that on the set of patterns with fixed eccentricity topological entropy attains its minimum at a unimodal \(X\) minimal pattern. Further the paper deals with properties of green patterns which include \(X\) minimal ones. Using the notion of complexity of a green pattern the author gives the best bounds for the topological entropy of a pattern of given complexity. Result concerning lower bounds for topological entropy of patterns with given eccentricity was independently proved in A. Blokh and M. Misiurewicz [Isr. J. Math. 102, 61-99 (1997; Zbl 0885.54016)] where rotation number and twist pattern instead of eccentricity and \(X\)-minimal pattern have been used. Reviewer: Katarina Janková (Bratislava) Cited in 1 ReviewCited in 1 Document MSC: 54H20 Topological dynamics (MSC2010) 26A18 Iteration of real functions in one variable 54C70 Entropy in general topology Keywords:interval map; topological entropy; cycle; pattern Citations:Zbl 0885.54016 PDFBibTeX XMLCite \textit{J. Bobok}, Fundam. Math. 162, No. 1, 1--36 (1999; Zbl 0938.54037) Full Text: EuDML