00-99 Jacques Rougemont
$\epsilon$-entropy estimates for driven parabolic equations (902K, Postscript) Mar 4, 00
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 00-99.src( 00-99.keywords , attractor.ps )