Classification of permutations and cycles of maximum topological entropy
Tóm tắt
Iff is a continuous self-map of a compact interval we can represent each finite fully invariant set off by a permutation. We can then calculate the topological entropy of the permutation. This provides us with a numerical measure of complexity for any map which exhibits a given permutation type. In this paper we present cyclic and noncyclic permutations which have maximum topological entropy amongst all cyclic or noncyclic permutations of the same length.
Tài liệu tham khảo
L. Block andW. A. Coppel,Dynamics in One Dimension, Lecture Notes in Math.,1513, Springer-Verlag, Berlin and New York, (1992).
L. Block, J. Guckenheimer, M. Misiurewicz andL. S. Young,Periodic points and topological entropy for one-dimensional maps. Lecture Notes in Math.,819, Springer-Verlag, Berlin and New York, (1980), 18–34.
W. Geller andJ. Tolosa,Maximal Entropy Odd Orbit Types. Transactions Amer. Math. Soc.,329, No. 1, (1992), 161–171.
W. Geller andB. Weiss,Uniqueness of maximal entropy odd orbit types. Proc. Amer. Math. Soc.,123, No. 6, (1995), 1917–1922.
W. Geller andZ. Zhang,Maximal entropy permutations of even size. Proc. Amer. Math. Soc.,126, No. 12, (1998), 3709–3713.
I. Jungreis,Some Results on the Sarkovskii Partial Ordering of Permutations. Transactions Amer. Math. Soc.,325, No. 1, (1991), 319–344.
D. M. King,Maximal entropy of permutations of even order. Ergod. Th. and Dynam. Sys.,17, No. 6, (1997), 1409–1417.
D. M. King,Non-uniqueness of even order permutations with maximal entropy. Ergod. Th. and Dynam. Sys.,20, (2000), 801–807.
D. M. King and J. B. Strantzen,Maximum entropy of cycles of even period. Mem. Amer. Math. Soc.,152, No. 723, 2001.
D. M. King and J. B. Strantzen,Cycles of period 4k which attain maximum topological entropy. (submitted for publication).
M. Misiurewicz and Z. Nitecki,Combinatorial Patterns for maps of the Interval. Memoirs Amer. Math. Soc.,94, No. 456, (1991).
M. Misiurewicz andW. Szlenk,Entropy of piecewise monotone mappings. Studia Math.,67, (1980), 45–63.