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January  2010, 13(1): 117-127. doi: 10.3934/dcdsb.2010.13.117

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, China, China

Received  November 2008 Revised  June 2009 Published  October 2009

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.
Keywords: hyperbolic set, $C^{0}$ random perturbation., flow.
Mathematics Subject Classification: Primary: 37D20; Secondary: 37H9.
Citation: Qiuxia Liu, Peidong Liu. Topological stability of hyperbolic sets of flows under random perturbations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 117-127. doi: 10.3934/dcdsb.2010.13.117
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