Affiliations: Institute für Angewandte Mathematik der Universität Bonn, Wegelerstrasse 6, D-53115, Bonn, Germany; SFB 611; BiBoS IZKS; CERFIM (Locamo); Acc. Arch. (USI) (Mendrisio); Dip. Matematica, Universita di Trento E-mail: albeverio@uni-bonn.de | Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, 119526 Moscow, Russia E-mail: {dobr;poter}@ipmnet.ru, poterma@rambler.ru
Note: [] Corresponding author. Laboratory for Mathematical Methods in Mechanics, Institute for Problems in Mechanics, pr. Vernadskogo 101-1, 119526, Moscow, Russia; Fax: +7 095 9382048.
Abstract: Smooth vector fields V in \[$\mathbb{R}$n having a k-dimensional invariant torus are considered and the possibility of constructing the asymptotic eigenfunctions localized in the neighborhood of this torus is analyzed for the case of a corresponding small diffusion operator V·∇−εΔ, ε>0. The asymptotic stability property of the invariant torus is a sufficient condition for the existence of such eigenfunctions. Both the regular case (where the variational system is reducible) and the nonregular case (where the variational system is nonreducible) are considered.
