Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2009; 46(2): 225-236

Printed March 1, 2009

Copyright © The Korean Mathematical Society.

Complexity of continuous semi-flows and related dynamical properties

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

Hebei Normal University, Hebei Normal University, and Beijing University

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

MSC numbers: 37B05, 34C28