COMPLEXITY OF CONTINUOUS SEMI-FLOWS AND RELATED DYNAMICAL PROPERTIES

- Journal title : Journal of the Korean Mathematical Society
- Volume 46, Issue 2, 2009, pp.225-236
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2009.46.2.225

Title & Authors

COMPLEXITY OF CONTINUOUS SEMI-FLOWS AND RELATED DYNAMICAL PROPERTIES

Zhang, Feng; He, Lian-Fa; Lu, Qi-Shao;

Zhang, Feng; He, Lian-Fa; Lu, Qi-Shao;

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;

Language

English

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