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Topological entropy of the induced maps of the inverse limits with bonding maps. (English) Zbl 0838.54017

Summary: We generalize a result of R. Bowen [Proc. Sympos. Pure Math. 14, 23-41 (1970; Zbl 0207.54402)] by showing that the topological entropy of the induced map of the inverse limit space with bonding maps is equal to the limit of the topological entropy of the original maps. As an application we prove that the topological entropy of each induced homeomorphism of a hereditarily decomposable chainable continuum is zero and then generalize some known result of M. Barge and J. Martin [Trans. Am. Math. Soc. 289, 355-365 (1985; Zbl 0559.58014)].

MSC:

54C70 Entropy in general topology
54H20 Topological dynamics (MSC2010)
54F15 Continua and generalizations
26A18 Iteration of real functions in one variable
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