00-99 Jacques Rougemont

$\epsilon$-entropy estimates for driven parabolic equations (902K, Postscript) Mar 4, 00

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Abstract. We consider parabolic evolution equations on unbounded domains driven by additive coupling to an independent dynamical system. We define the attractor of the combined system and estimate its Kolmogorov $\epsilon $--entropy (the coarse-grained spatial density of active modes with mesh size $\epsilon$). The total $\epsilon$--entropy is at most $\OO(\log\epsilon ^{-1})$ larger then the $\epsilon$--entropy of the driving system. An example of a system whose $\epsilon $--entropy is strictly larger than that of the driving system is constructed. Remarks on the behaviour of the entropy under spatial scaling are made.

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