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http://dx.doi.org/10.4134/JKMS.2009.46.2.225

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)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 225-236 More about this Journal
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.
Keywords
continuous semi-flow; spanning set; complexity function; pointwise scattering; scattering;
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