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EQUI-ATTRACTION AND THE CONTINUOUS DEPENDENCE OF ATTRACTORS ON PARAMETERS

Published online by Cambridge University Press:  15 January 2004

LI DESHENG  and
P. E. KLOEDEN
LI DESHENG
Affiliation:
Department of Mathematics and Information Science, Yantai University, Yantai 264005, Shandong, People's Republic of China e-mail: [email protected]
P. E. KLOEDEN
Affiliation:
FB Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany e-mail: [email protected]
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Abstract

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The equi-attraction properties concerning the global attractors $\a_\lam$ of dynamical systems $S_\lam(t)$ with parameter $\lam\in\Lam$, where $\Lam$ is a compact metric space, are investigated. In particular, under appropriate conditions, it is shown that the equi-attraction of the family $\{\a_\lam\}$ is equivalent to the continuity of $\a_\lam$ in $\lam$ with respect to the Hausdorff distance.

Keywords

Primary 47J2537L3034C20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 1 , January 2004 , pp. 131 - 141
Copyright
2004 Glasgow Mathematical Journal Trust