## Mean proximality and mean Li-Yorke chaos

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- by Felipe Garcia-Ramos and Lei Jin PDF
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**145**(2017), 2959-2969 Request permission

## 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.## References

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## Additional Information

**Felipe Garcia-Ramos**- Affiliation: Instituto de Fisica, Universidad Autonoma de San Luis Potosi, Av. Manuel Nava 6, SLP, 78290 Mexico
- MR Author ID: 969565
- Email: felipegra@yahoo.com
**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
- Email: jinleim@mail.ustc.edu.cn
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 2959-2969 - MSC (2010): Primary 37B05, 54H20
- DOI: https://doi.org/10.1090/proc/13440
- MathSciNet review: 3637944