Gabriel J Lord, Jacques Rougemont
Topological and $\epsilon$-entropy for Large Volume 
Limits of Discretised Parabolic Equations
(254K, Postscript)

ABSTRACT.  We consider semi-discrete and fully discrete 
approximations of nonlinear parabolic equations in the limit of 
unbounded domains, which by a scaling argument is equivalent to the 
limit of small viscosity. We define the spatial density of $\epsilon 
$-entropy, topological entropy and dimension for the attractors and 
show that these quantities are bounded. We also provide practical 
means of computing lower bounds on them. The proof uses the property 
that solutions lie in 
Gevrey classes of analyticity, which we 
define in a way that does not depend on the size of the spatial 
domain. As a specific example we discuss the complex Ginzburg-Landau 
equation.