On the dynamics of flows on compact metric spaces

Jaeyoo Choy; Hahng-Yun Chu

doi:10.3934/cpaa.2010.9.103

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2010, Volume 9, Issue 1: 103-108. Doi: 10.3934/cpaa.2010.9.103

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On the dynamics of flows on compact metric spaces

Jaeyoo Choy^1, and
Hahng-Yun Chu^2,

1.
Department of Mathematics, Kyungpook National University, Sankyuk-dong, Buk-gu, Daegu 702-701
2.
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Gwahak-ro, Yuseong-gu, Daejeon 305-701

Received: January 31, 2009

Revised: June 30, 2009

Published: December 2009

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Abstract

In this paper, we consider a (generalized) envelope of flows on compact metric spaces. This partly generalizes the notion of envelope of maps in discrete geometry ([3]). We clarify a certain distinction between the flow geometry and the discrete one, which is explained by showing that any !-limit set for an envelope of flows is an empty set, whereas it is nonempty in general in discrete case.

Keywords:

Envelope,
flow,
$\omega$-limit sets.

Mathematics Subject Classification: 37B05, 54H20.

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