Distributional chaos for continuous mappings of the circle
Abstract
We show that theory of distributional chaos for continuous functions on the unit interval as developed recently by Schweizer and Smítal remains essentially true for continuous mappings of the circle, with natural exceptions.
References
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2. L.S. Block, E.M. Coven, I. Mulvey, Z. Nitecki, Homoclinic and nonwandering points for maps of the circle, Ergodic Theory Dynamical Systems 3 (1983), 521-532.
3. L.S. Block, J. Guckenheimer, M. Misiurewicz, L.S. Young, Periodic points and topological entropy of one-dimensional maps, in Global theory of dynamical systems (Proc. Internat. Conf., Univ., Evanston, III., 1979, 18-34.) Lecture Notes in Math. 812 Springer, Berlin 1980.
4. L.S. Block, Periods of periodic points of maps of the circle which have a fixed point, Proc. Amer. Math. Soc. 82 (1981), 481-486.
5. M. Kuchta, Characterization of chaos for continuous maps of circle, Comment. Math. Univ. Carolinea 31 (1990), 388-391.
6. G. Liao, Q. Fan, Minimal subshift which display Schweizer-Smítal chaos and have zero topological entropy, Science in China 41 (1998), 33-38.
7. M. Misiurewicz, Periodic points of maps of degree one of a circle, Ergodic Theory Dynamical Systems 2 (1982), 221-227.
8. B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), 737-754.
MálekM. (1999). Distributional chaos for continuous mappings of the circle. Annales Mathematicae Silesianae, 13, 205-210. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14149
Michal Málek
Michal.Malek@math.slu.cz
Institute of Mathematics, Silesian University in Opava, Czech Republic Czechia
Institute of Mathematics, Silesian University in Opava, Czech Republic Czechia
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