Entropy of semipatterns or how to connect the dots to minimize entropy
HTML articles powered by AMS MathViewer
- by Jonathan Ashley, Ethan M. Coven and William Geller PDF
- Proc. Amer. Math. Soc. 113 (1991), 1115-1121 Request permission
Abstract:
In this paper we solve the following problem: Given a map $\varphi$ from a finite subset of the reals into the reals, how do you connect the dots in the graph of $\varphi$ in order to minimize the topological entropy of the resulting map of the interval?References
-
L. Alseda, J. Llibre, M. Misiurewicz, and C. Simo, Rotation intervals for a class of maps of the real line to itself, Ergodic Theory Dynamical Systems 6 (1986), 117-132.
- John Milnor and William Thurston, On iterated maps of the interval, Dynamical systems (College Park, MD, 1986–87) Lecture Notes in Math., vol. 1342, Springer, Berlin, 1988, pp. 465–563. MR 970571, DOI 10.1007/BFb0082847
- MichałMisiurewicz, Horseshoes for mappings of the interval, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 2, 167–169 (English, with Russian summary). MR 542778
- MichałMisiurewicz, Jumps of entropy in one dimension, Fund. Math. 132 (1989), no. 3, 215–226. MR 1002409, DOI 10.4064/fm-132-3-215-226
- MichałMisiurewicz and Zbigniew Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 94 (1991), no. 456, vi+112. MR 1086562, DOI 10.1090/memo/0456
- M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980), no. 1, 45–63. MR 579440, DOI 10.4064/sm-67-1-45-63
- B. L. van der Waerden, Modern Algebra. Vol. I, Frederick Ungar Publishing Co., New York, N. Y., 1949. Translated from the second revised German edition by Fred Blum; With revisions and additions by the author. MR 0029363
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 1115-1121
- MSC: Primary 58F03; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1991-1086320-3
- MathSciNet review: 1086320