Topological stability of hyperbolic sets of flowsunder random perturbations

Qiuxia Liu; Peidong Liu

doi:10.3934/dcdsb.2010.13.117

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2010, Volume 13, Issue 1: 117-127. Doi: 10.3934/dcdsb.2010.13.117

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Topological stability of hyperbolic sets of flows under random perturbations

Qiuxia Liu^1, and
Peidong Liu^1,

1.
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871

Received: October 31, 2008

Revised: May 31, 2009

Published: June 2010

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Abstract

In this paper we consider $C^{0}$ random perturbations of a hyperbolic set of a flow. We show that the hyperbolic set is structurally semi-stable under such perturbations.

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Mathematics Subject Classification: Primary: 37D20; Secondary: 37H99.

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