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On the notion of random chaos


Author: Jan Andres
Journal: Proc. Amer. Math. Soc. 145 (2017), 3423-3435
MSC (2010): Primary 37D45, 37E15; Secondary 37H10
DOI: https://doi.org/10.1090/proc/13464
Published electronically: January 25, 2017
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Abstract: Deterministic chaos is investigated for random dynamical systems in dimension one. Some well-known as well as new Li-Yorke-type theorems are randomized. Deterministic chaos exhibited by random dynamics is therefore called random chaos for brevity. Chaotic random dynamics are also studied for multivalued maps.


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Additional Information

Jan Andres
Affiliation: Department of Mathematical Analysis and Application of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
Email: jan.andres@upol.cz

DOI: https://doi.org/10.1090/proc/13464
Keywords: Random chaos, deterministic chaos, randomization, chaotic random dynamics, random periodic orbits, multivalued maps
Received by editor(s): February 11, 2016
Received by editor(s) in revised form: September 6, 2016
Published electronically: January 25, 2017
Additional Notes: The author was supported by the grant No. 14-06958S “Singularities and impulses in boundary value problems for nonlinear ordinary differential equations” of the Grant Agency of the Czech Republic.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society