Abstract
TheD-function is a new topological invariant introduced by the author in [3] to classify the minimal dynamical system and to generalize Sharkovskii's theorem on the coexistence of periodic orbits. We show that theD-function and the topological entropy are independent.
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References
F. Hahn and Y. Katznelson, “On the entropy of uniquely ergodic transformations,“Trans. Amer. Math. Soc.,126, 335–360 (1967).
C. Grillenberger, “Constructions of strictly ergodic system. I. Given entropy,“Z. Wahrscheinlichkeitstheorie,25, 323–334 (1973).
Xiangdong Ye, “D-functions of a minimal set and coexistence of almost periodic points of interval mapping,“Ergod. Theory Dynam. Syst.,12, 365–376 (1992).
W. H. Gottshalk, “Powers of homeomorphisms with almost periodic properties,“Bull. Amer. Math. Soc.,50, 222–227 (1944).
R. L. Adler, A. C. Honheim, and M. H. McAndrew, “Topological entropy,“Trans. Amer. Math. Soc,144, 309–319 (1965).
P. Walters,An Introduction to Ergodic Theory, Springer, Berlin-New York (1982).
Xiangdong Ye,Coexistence of Uniquely Ergodic Subsystems of Interval Mapping, Preprint (1990).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 2, pp. 287–292, February, 1993.
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Ye, X. Minimal dynamical system with givenD-function and topological entropy. Ukr Math J 45, 309–315 (1993). https://doi.org/10.1007/BF01060988
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DOI: https://doi.org/10.1007/BF01060988