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February  2005, 12(2): 213-232. doi: 10.3934/dcds.2005.12.213

Uniform attractors of periodic and asymptotically periodic dynamical systems

P.E. Kloeden 1, , Desheng Li 2, and  Chengkui Zhong 3,

1. 

FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.
2. 

Department of Mathematics and Information Science, Yantai University, Yantai 264005, China
3. 

Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, China

Received  August 2003 Revised  July 2004 Published  December 2004

The uniform forward global attractors of periodic systems and the comparison of the dynamics between asymptotically periodic non-autonomous dynamical systems and their corresponding limiting periodic processes are investigated. The existence and Lyapunov stability of such attractors are established and a Lyapunov functional charecterization of uniform forward global attractors of non-autonomous periodic processes is presented. The results are illustrated with examples of ordinary and delay differential equations.
Keywords: uniform global attractor, semiuniform global attractor, Uniform forward global attractor, asymptotically periodic process., periodic process.
Mathematics Subject Classification: 47H17, 58F03, 34C20, 34D2.
Citation: P.E. Kloeden, Desheng Li, Chengkui Zhong. Uniform attractors of periodic and asymptotically periodic dynamical systems. Discrete & Continuous Dynamical Systems, 2005, 12 (2) : 213-232. doi: 10.3934/dcds.2005.12.213
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