대한수학회지 (Journal of the Korean Mathematical Society)

  • 제45권1호
  • /
  • Pages.221-228
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  • 2008
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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TOPOLOGICAL COMPLEXITY OF SEMIGROUP ACTIONS

  • Yan, Xinhua (College of Mathematics and Information Science Hebei Normal University) ;
  • He, Lianfa (College of Mathematics and Information Science Hebei Normal University)
  • 발행 : 2008.01.31
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초록

In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.

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참고문헌

  1. S. Ferenczi, Measure-theoretic complexity of ergodic systems, Israel J. Math. 100 (1997), 189-207 https://doi.org/10.1007/BF02773640
  2. S. Ferenczi, Complexity of sequences and dynamical systems, Discrete Math. 206 (1999), no. 1-3, 145-154 https://doi.org/10.1016/S0012-365X(98)00400-2
  3. F. Blanchard, B. Host, and A. Maass, Topological complexity,Ergodic Theory Dynam. Systems 20 (2000), no. 3, 641-662 https://doi.org/10.1017/S0143385700000341
  4. K. E. Petersen, Disjointness and weak mixing of minimal sets, Proc. Amer. Math. Soc. 24 (1970), 278-280 https://doi.org/10.2307/2036347
  5. J. de Vries, Elements of topological dynamics, Mathematics and its Applications, 257. Kluwer Academic Publishers Group, Dordrecht, 1993

피인용 문헌

  1. Topological entropy of formal languages vol.94, pp.3, 2017, https://doi.org/10.1007/s00233-016-9782-0