Almost everywhere reducibility of quasi-periodic fibered flows with values in compact groups. (Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compacts.) (French) Zbl 1098.37510

Summary: Let us be given a compact “semisimple” Lie group \(G\) with Lie algebra \(g\), a regular element \(A\in g\), a bounded interval \(\Lambda\subset\mathbb R\) and a diophantine vector \(\omega\in\mathbb R^d\); then if \(F \in C^\omega(\mathbb R^d/\mathbb Z^d,g)\) is small enough, \(\omega\) meaning here “real analytic”, for Lebesgue-a.e. \(\lambda\in\Lambda\), the quasi-periodic system \(\lambda A+F((\omega_1/2\pi),\dots, (\omega_d/2\pi))\), with frequency vector \(\omega\), is Floquet-reducible modulo some finite covering depending only on the group \(G\). This theorem is a generalization of the one proved in the author’s monograph [Reducibility of skew-product systems with values in compact groups (French), Astérisque 259, Paris: SMF (1999; Zbl 0957.37016)].


37C55 Periodic and quasi-periodic flows and diffeomorphisms
37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations


Zbl 0957.37016
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