 013 Hans Henrik Rugh
 Coupled Maps and Analytic Function Spaces
(530K, Postscript)
Jan 4, 01

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider realanalytic couplings of a direct product of uniformly
analytic and expanding circle maps. We show that when the coupling
is sufficiently small the dynamical system carries a natural invariant
measure which is ergodic and for which time correlations decay
exponentially fast. When a spatial decay of the couplings is present
this is reflected in a spatial decay of correlations in the marginal
densities of the invariant measure, e.g.\ polynomial decay may arise
from a polynomial decay of the couplings. The allowable couplings
include sums of pair, or more generally, $n$point, interactions
whose norms are summable with a small enough sum.
The space of couplings and the observable algebra
are Banach algebras of functions which are analytic
in infinitely many variables. These algebras act in a natural way
on a Banach module of complex measures with analytic marginal
densities. Using a simple resummation formula we obtain uniform bounds
for a Perron Frobenius operator associated with the coupled map.
We calculate explicit bounds in some examples.
 Files:
013.src(
013.keywords ,
cml111.ps )