Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMPLEXITY OF CONTINUOUS SEMI-FLOWS AND RELATED DYNAMICAL PROPERTIES

  • Zhang, Feng (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HEBEI NORMAL UNIVERSITY, SCHOOL OF SCIENCE BEIJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS) ;
  • He, Lian-Fa (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HEBEI NORMAL UNIVERSITY) ;
  • Lu, Qi-Shao (SCHOOL OF SCIENCE BEIJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS)
  • Published : 2009.03.31
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Abstract

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

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References

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