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January  2010, 9(1): 103-108. doi: 10.3934/cpaa.2010.9.103

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, South Korea
2. 

Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Gwahak-ro, Yuseong-gu, Daejeon 305-701, South Korea

Received  February 2009 Revised  July 2009 Published  October 2009

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, $\omega$-limit sets., flow.
Mathematics Subject Classification: 37B05, 54H2.
Citation: Jaeyoo Choy, Hahng-Yun Chu. On the dynamics of flows on compact metric spaces. Communications on Pure and Applied Analysis, 2010, 9 (1) : 103-108. doi: 10.3934/cpaa.2010.9.103
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