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On entropy of patterns given by interval maps. (English) Zbl 0938.54037

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.

MSC:

54H20 Topological dynamics (MSC2010)
26A18 Iteration of real functions in one variable
54C70 Entropy in general topology

Citations:

Zbl 0885.54016
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