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Mean proximality and mean Li-Yorke chaos

Authors: Felipe Garcia-Ramos and Lei Jin
Journal: Proc. Amer. Math. Soc. 145 (2017), 2959-2969
MSC (2010): Primary 37B05, 54H20
Published electronically: December 27, 2016
MathSciNet review: 3637944
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Abstract: We prove that if a topological dynamical system is mean sensitive and contains a mean proximal pair consisting of a transitive point and a periodic point, then it is mean Li-Yorke chaotic (DC2 chaotic). On the other hand we show that a system is mean proximal if and only if it is uniquely ergodic and the unique measure is supported on one point.

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Felipe Garcia-Ramos
Affiliation: Instituto de Fisica, Universidad Autonoma de San Luis Potosi, Av. Manuel Nava 6, SLP, 78290 Mexico
MR Author ID: 969565

Lei Jin
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Institute of Mathematics, Polish Academy of Sciences, Warsaw 00656, Poland

Keywords: Mean Li-Yorke chaos, mean Devaney chaos, mean Li-Yorke set, mean proximal pair, mean asymptotic pair
Received by editor(s): March 5, 2016
Received by editor(s) in revised form: August 8, 2016
Published electronically: December 27, 2016
Additional Notes: The first author was supported by IMPA, CAPES (Brazil) and NSERC (Canada). The second author was supported by NNSF of China 11225105, 11371339 and 11431012, and was partially supported by the NCN (National Science Center, Poland) grant 2013/08/A/ST1/00275.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society