Distributional (and other) chaos and its measurement. (English) Zbl 1012.37022

Schweizer, B.; Sklar, A.; Smítal, J.

Real Anal. Exch. 26(2000-2001), No. 2, 495-524 (2001).

The paper presents the recently introduced by the authors [B. Schweizer and J. Smítal, Trans. Am. Math. Soc. 344, No. 2, 737-754 (1994; Zbl 0812.58062)] notion of distributional chaos. The main goal is to introduce this notion for wider audience and to illustrate it with many examples. The comparison with some earlier definitions is also given.

Reviewer: Sergiy Yanchuk (Kyïv)

MSC:

37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37E05	Dynamical systems involving maps of the interval
54H20	Topological dynamics (MSC2010)
26A18	Iteration of real functions in one variable
54E70	Probabilistic metric spaces

Keywords:

distributional chaos; topological entropy; invariant measures; Li-Yorke chaos

Citations:

Zbl 0812.58062