Reducibility of ultra-differentiable quasiperiodic cocycles under an adapted arithmetic condition

DOI10.1090/proc/15433OpenAlexW3159752387MaRDI QIDQ4990353

Claire Chavaudret, Shuqing Liang, Abed Bounemoura

Publication date: 28 May 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.06411

zbMATH Keywords

KAM theoryultra-differentiable functionsreducibility of quasiperiodic cocycle

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Relations between ergodic theory and number theory (37A44)

Related Items (5)

Reducibility in a certain matrix Lie algebra for smooth linear quasi-periodic system ⋮ Almost reducibility of quasiperiodic \(SL(2, \mathbb{R})\)-cocycles in ultradifferentiable classes ⋮ Optimal linearization of vector fields on the torus in non-analytic Gevrey classes ⋮ Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications ⋮ Linearization of ultra-differentiable circle flows beyond Brjuno condition

Cites Work

• Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition
• KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character
• An extension of a result by Dinaburg and Sinai on quasi-periodic potentials
• Full measure reducibility for generic one-parameter family of quasi-periodic linear systems
• The rotation number for almost periodic potentials
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems
• Linearization of Gevrey flows on \(\mathbb{T}^d\) with a Brjuno type arithmetical condition
• KAM à la R
• Reducibility of quasiperiodic cocycles in linear Lie groups
• KAM, α-Gevrey regularity and the α-Bruno-Rüssmann condition
• Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compacts
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