Ye, Xiangdong Topological entropy of the induced maps of the inverse limits with bonding maps. (English) Zbl 0838.54017 Topology Appl. 67, No. 2, 113-118 (1995). 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)]. Cited in 1 ReviewCited in 12 Documents MSC: 54C70 Entropy in general topology 54H20 Topological dynamics (MSC2010) 54F15 Continua and generalizations 26A18 Iteration of real functions in one variable Keywords:induced map; inverse limit space; topological entropy; induced homeomorphism; hereditarily decomposable chainable continuum Citations:Zbl 0207.54402; Zbl 0559.58014 PDF BibTeX XML Cite \textit{X. Ye}, Topology Appl. 67, No. 2, 113--118 (1995; Zbl 0838.54017) Full Text: DOI OpenURL References: [1] Barge, M.; Martin, J., Chaos, periodicity, and snakelike continua, (), 355-365 · Zbl 0559.58014 [2] Bowen, R., Topological entropy and axiom A, (), 23-41 · Zbl 0207.54402 [3] Bowen, R.; Franks, J., The periodic points of maps of the disk and the interval, Topology, 15, 337-342, (1976) · Zbl 0346.58010 [4] () [5] Kuratowski, K., (), Polish Scientific Publishers, Warsaw [6] Li, S., Dynamical properties of the shift maps on the inverse limit spaces, Ergodic theory dynamical systems, 12, 95-108, (1992) · Zbl 0767.58029 [7] Misiurewicz, M., Horseshoes for mappings of the interval, Bull. acad. polon. sci. ser. sci. math., 27, 167-169, (1979) · Zbl 0459.54031 [8] Nadler, S.B., Continuum theory, () · Zbl 0757.54009 [9] Read, D.R., Confluent and related mappings, (), 233-239 · Zbl 0247.54010 [10] Walters, P., An introduction to ergodic theory, (1982), Springer New York · Zbl 0475.28009 [11] Williams, R., One-dimensional nonwandering set, Topology, 6, 473-487, (1967) · Zbl 0159.53702 [12] Ye, X., The dynamics of homeomorphisms of hereditarily decomposable chainable continua, Topology appl., 64, 85-93, (1995) · Zbl 0831.54019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.