Uniqueness of maximal entropy odd orbit types

Geller, William; Weiss, Benjamin

doi:10.1090/S0002-9939-1995-1249876-7

Uniqueness of maximal entropy odd orbit types

Authors: William Geller and Benjamin Weiss
Journal: Proc. Amer. Math. Soc. 123 (1995), 1917-1922
MSC: Primary 58F20; Secondary 58F08
DOI: https://doi.org/10.1090/S0002-9939-1995-1249876-7
MathSciNet review: 1249876
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the maximal entropy orbit types of odd period for interval maps are unique. In fact we prove that they are uniquely maximal among all (not necessarily cyclic) permutations.

[Be] Chris Bernhardt, The ordering on permutations induced by continuous maps of the real line, Ergodic Theory Dynam. Systems 7 (1987), no. 2, 155–160. MR 896787, https://doi.org/10.1017/S0143385700003898
[BCop] L. S. Block and W. A. Coppel, Dynamics in one dimension, Lecture Notes in Mathematics, vol. 1513, Springer-Verlag, Berlin, 1992. MR 1176513
[BGMY] Louis Block, John Guckenheimer, Michał Misiurewicz, and Lai Sang Young, Periodic points and topological entropy of one-dimensional maps, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979) Lecture Notes in Math., vol. 819, Springer, Berlin, 1980, pp. 18–34. MR 591173
[GT] William Geller and Juán Tolosa, Maximal entropy odd orbit types, Trans. Amer. Math. Soc. 329 (1992), no. 1, 161–171. MR 1020040, https://doi.org/10.1090/S0002-9947-1992-1020040-1
[J] Irwin Jungreis, Some results on the Šarkovskiĭ partial ordering of permutations, Trans. Amer. Math. Soc. 325 (1991), no. 1, 319–344. MR 998354, https://doi.org/10.1090/S0002-9947-1991-0998354-X
[MN] Michał Misiurewicz and Zbigniew Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 94 (1991), no. 456, vi+112. MR 1086562, https://doi.org/10.1090/memo/0456