Weakly almost periodic points and chaotic dynamics of discrete amenable group actions
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The aim of this paper is to introduce the notions of (quasi) weakly almost periodic point, measure center and minimal center of attraction of amenable group actions, explore the connections of levels of the orbit's topological structure of (quasi) weakly almost periodic points and study chaotic dynamics of transitive systems with full measure centers. Actually, we showed that weakly almost periodic points and quasi-weakly almost periodic points have distinct orbit's topological structure and proved that there exists at least countable Li-Yorke pairs if the system contains a proper (quasi) weakly almost periodic point and that a transitive but not minimal system with a full measure center is strongly ergodically chaotic.
Abstract
The aim of this paper is to introduce the notions of (quasi) weakly almost periodic point, measure center and minimal center of attraction of amenable group actions, explore the connections of levels of the orbit's topological structure of (quasi) weakly almost periodic points and study chaotic dynamics of transitive systems with full measure centers. Actually, we showed that weakly almost periodic points and quasi-weakly almost periodic points have distinct orbit's topological structure and proved that there exists at least countable Li-Yorke pairs if the system contains a proper (quasi) weakly almost periodic point and that a transitive but not minimal system with a full measure center is strongly ergodically chaotic.
참고문헌 (13)
- L. N. Argabright, "Semigroups satisfying a strong F lner condition", Proc. Amer. Math. Soc, 18, pp.587~591 (1967)
- J. Auslander, "Minimal ows and their extensions" (1988), North-Holland Publishing Co
- Z. Chen, "Chaotic dynamics of minimal center of attraction of discrete amenable group actions", J. Math. Anal. Appl, 456(2), pp.1397~1414 (2017)
- A. H. Dooley, "The spectrum of completely positive entropy actions of countable amenable groups", J. Funct. Anal, 196(1), pp.1~18 (2002)
- N. Higson, "Amenable group actions and the Novikov conjecture", J. Reine Angew. Math, 519, pp.143~153 (2000)
- W. Huang, "Local entropy theory for a countable discrete amenable group action", J. Funct. Anal, 261(4), pp.1028~1082 (2011)
- Y. Huang, "Two new recurrent levels for C0-ows", Acta Appl. Math, 118, pp.125~145 (2012)
- E. Lindenstrauss, "Pointwise theorems for amenable groups", Invent. Math, 146(2), pp.259~295 (2001)
- C. C. Moore, "Amenable subgroups of semisimple groups and proximal ows", Israel J. Math, 34(1-2), pp.121~138 (1979)
- P. Walters, "An Introduction to Ergodic Theory" (1982), Springer-Verlag
- J. Yin, "Weakly almost periodic points and some chaotic properties of dynamical systems", Internat. J. Bifur. Chaos Appl. Sci. Engrg, 25(9), pp.1550115~ (2015)[DOI]
- Z. L. Zhou, "Weakly almost periodic point and measure centre", Sci. China Ser. A, 36(2), pp.142~153 (1993)
- Z. L. Zhou, "Level of the orbit's topological structure and topological semi-conjugacy", Sci. China Ser. A, 38(8), pp.897~907 (1995)