Jacques Rougemont
$\epsilon$-entropy estimates for driven parabolic equations
(902K, Postscript)

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.