The perturbation of attractors  of skew-product flows with a shadowing driving system

P.E. Kloeden; Victor S. Kozyakin

doi:10.3934/dcds.2001.7.883

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2001, Volume 7, Issue 4: 883-893. Doi: 10.3934/dcds.2001.7.883

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The perturbation of attractors of skew-product flows with a shadowing driving system

P.E. Kloeden^1, and
Victor S. Kozyakin^2,

1.
FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.
2.
Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoj Karetny lane, 19, 101447 Moscow

Received: October 31, 2000

Revised: March 31, 2001

Published: September 2001

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Abstract

The influence of the driving system on a skew-product flow generated by a triangular system of differential equations can be perturbed in two ways, directly by perturbing the vector field of the driving system component itself or indirectly by perturbing its input variable in the vector field of the coupled component. The effect of such perturbations on a nonautonomous attractor of the driven component is investigated here. In particular, it is shown that a perturbed nonautonomous attractor with nearby components exists in the indirect case if the driven system has an inflated nonautonomous attractor and that the direct case can be reduced to this case if the driving system is shadowing.

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Mathematics Subject Classification: 34D10, 34D45, 37C60.

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