Finite-Dimensional Functional Analysis Applied to Transfer Operators for Infinite-Dimensional Maps
2002, v.8, №2, 149-154
We describe a simple approach to perturbative analysis of Perron - Frobenius operators and study the Floquet spectrum of the transfer operators of weakly coupled analytic maps on an infinite lattice: we are able to go beyond the first spectral gap and to exhibit smooth curves of eigenvalues and eigenvectors as functions of the crystal momenta. This talk given on January 23, 2001, at the session on Rapidity of convergence to equilibrium or stationary states, Journees Systemes Aleatoires Inhomogenes (Universite de Cergy-Pontoise, France) describes joint work with H.H. Rugh, Cergy-Pontoise. The detailed proofs of the results announced here, as well as further statements and references, may be found in [V. Baladi and H.-H. Rugh, Floquet spectrum of weakly coupled map lattices, Commun. Math. Phys., 2001, v. 220, 561-582].
Keywords: coupled map lattices,transfer operator,Floquet spectrum