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Experimental Mathematics Volume 17, 2008 - Issue 4
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Original Article

A Lower Bound for the Maximum Topological Entropy of (4k + 2)-Cycles

Lluís Alsedà Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona, Spain
,
David Juher Departament d'Informàtica i Matemàtica Aplicada, Universitat de Girona, Lluís Santaló s/n, 17071 Girona, Spain
&
Deborah M. King Department of Mathematics and Statistics, The University of Melbourne, Vic, 3010, Australia
Pages 391-407 | Published online: 30 Jan 2011

  • R. L. Adler, A. G. Konheim, and M. H. McAndrew. "Topological Entropy." Trans. Amer. Math. Soc. 114 (1965), 309-319.
  • Lluís Alsedà, Jaume Llibre, and Michał Misiurewicz. Combinatorial Dynamics and Entropy in Dimension One, 2nd ed., Advanced Series in Nonlinear Dynamics, 5. River Edge, NJ: World Scientific, 2000.
  • Stewart Baldwin. "Generalizations of a Theorem of Sarkovskii on Orbits of Continuous Real-Valued Functions." Discrete Math. 67:2 (1987), 111-127.
  • L. S. Block and W. A. Coppel. Dynamics in One Dimension, Lecture Notes in Mathematics 1513. Berlin: Springer-Verlag, 1992.
  • William Geller and Juán Tolosa. "Maximal Entropy Odd Orbit Types." Trans. Amer. Math. Soc. 329:1 (1992), 161-171.
  • William Geller and Benjamin Weiss. "Uniqueness of Maximal Entropy Odd Orbit Types." Proc. Amer. Math. Soc. 123:6 (1995), 1917-1922.
  • William Geller and Zhenhua Zhang. "Maximal Entropy Permutations of Even Size." Proc. Amer. Math. Soc. 126:12 (1998), 3709-3713.
  • Irwin Jungreis, "Some Results on the Šarkovskiĭ Partial Ordering of Permutations." Trans. Amer. Math. Soc. 325:1 (1991), 319-344.
  • Deborah M. King. "Maximal Entropy of Permutations of Even Order." Ergodic Theory Dynam. Systems 17:6 (1997), 1409-1417.
  • Deborah M. King. "Non-uniqueness of Even Order Permutations with Maximal Entropy." Ergodic Theory Dynam. Systems 20:3 (2000), 801-807.
  • Deborah M. King and John B. Strantzen. "Maximum Entropy of Cycles of Even Period." Mem. Amer. Math. Soc. 152:723 (2001).
  • Deborah M. King and John B. Strantzen. "Cycles of Period 4k Which Attain Maximum Topological Entropy. Preprint, 2005.
  • Michał Misiurewicz and Zbigniew Nitecki. "Combinatorial Patterns for Maps of the Interval." Mem. Amer. Math. Soc. 94:456 (1991).
  • A. N. Šarkovśkiň. "Coexistence of Cycles of a Continuous Mapping of the Line into Itself." Ukrain. Mat. Ž. 16 (1964), 61-71 (in Russian).
  • A. N. Šarkovśkiň. "Coexistence of Cycles of a Continuous Map of the Line into Itself," translated by J. Tolosa. In Thirty Years after Sharkovskiň's Theorem: New Perspectives (Murcia, 1994), pp. 1-11, World Sci. Ser. Nonlinear Sci. Ser. B Spec. Theme Issues Proc., 8. River Edge, NJ: World Sci., 1995.
  • E. Seneta. Non-negative Matrices and Markov Chains, Springer Series in Statistics. New York: Springer, 2006.

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