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Zbl 1015.34028
Eliasson, L.H.
Almost reducibility of linear quasi-periodic systems. (English)
[A] Katok, Anatole (ed.) et al., Smooth ergodic theory and its applications. Proceedings of the AMS summer research institute, Seattle, WA, USA, July 26-August 13, 1999. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 69, 679-705 (2001). ISBN 0-8218-2682-4/hbk

The author's abstract: Reducibility and almost reducibility of linear quasiperiodic systems are discussed. The author proves a result showing that when such a system is analytic and close to constant coefficients and has Diophantine quasiperiodic frequencies it is always almost reducible in the sense that it can be analytically conjugate to a system arbitrarily close to constant coefficients. It is discussed when this approach converges and gives full reducibility, and when it does not. The author studies in particular the quasiperiodic Schrödinger equation and skew-products on $SO(3,\bbfR)$, and the relevance of this result for the perturbation theory of lower-dimensional tori in Hamiltonian systems.
[Hans F.Günzler (Kiel)]

MSC 2000:: *34C20 Transformation of ODE and systems
34C27 Almost periodic solutions of ODE
81Q05 Closed and approximate solutions to quantum-mechanical equations
70H12 Periodic and almost periodic solutions
37J40 Perturbations, etc.
37C55 Periodic and quasiperiodic flows and diffeomorphisms
37H99 Random dynamical systems

Keywords: reducibility; skew products; Schrödinger equation; KAM; quasiperiodic; Hamiltonian systems

Cited in: Zbl 1166.34019 Zbl 1108.47032

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