01-3 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 real-analytic 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 re-summation formula we obtain uniform bounds for a Perron Frobenius operator associated with the coupled map. We calculate explicit bounds in some examples.

Files: 01-3.src( 01-3.keywords , cml111.ps )