 0099 Jacques Rougemont
 $\epsilon$entropy estimates for driven parabolic equations
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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 coarsegrained 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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