Almost reducibility of quasiperiodic SL(2,R)-cocycles in ultradifferentiable classes

Almost reducibility of quasiperiodic SL(2,R)-cocycles in ultradifferentiable classes

Given a quasiperiodic cocycle in sl(2,R) sufficiently close to a constant, we prove that it is almost reducible in ultradifferentiable class under an adapted arithmetic condition on the frequency vector.

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Veröffentlicht in:Journal of Differential Equations 2023-05, Vol.356, p.243-288
Hauptverfasser: Chatal, Maxime, Chavaudret, Claire
Format: Artikel
Sprache:eng
Schlagworte:
Almost reducibility
Brjuno-Rüssmann condition
Dynamical Systems
KAM method
Mathematics
Quasi-periodic cocycles
Small divisors
Ultradifferentiable class
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Zusammenfassung:Given a quasiperiodic cocycle in sl(2,R) sufficiently close to a constant, we prove that it is almost reducible in ultradifferentiable class under an adapted arithmetic condition on the frequency vector.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2023.01.041