Chaotic functions with zero topological entropy
Author:
J. Smítal
Journal:
Trans. Amer. Math. Soc. 297 (1986), 269-282
MSC:
Primary 58F13; Secondary 54H20, 58F11
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849479-9
MathSciNet review:
849479
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Recently Li and Yorke introduced the notion of chaos for mappings from the class , where
is a compact real interval. In the present paper we give a characterization of the class
of mappings chaotic in this sense. As is well known,
contains the mappings of positive topological entropy. We show that
contains also certain (but not all) mappings that have both zero topological entropy and infinite attractors. Moreover, we show that the complement of
consists of maps that have only trajectories approximate by cycles. Finally, it turns out that the original Li and Yorke notion of chaos can be replaced by (an equivalent notion of)
-chaos, distinguishable on a certain level
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849479-9
Article copyright:
© Copyright 1986
American Mathematical Society