Resummation of perturbation series and reducibility for Bryuno skew-product flows

Abstract

We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.

30 pages, 12 figures

References in corpus (5)

• Hyperbolic low-dimensional invariant tori and summations of divergent series
• Reducibility or non-uniform hyperbolicity for quasiperiodic Schrodinger cocycles
• Fractional Lindstedt series
• Stability for quasi-periodically perturbed Hill's equations
• Degenerate lower-dimensional tori under the Bryuno condition

Cited by in corpus (6)

• Response solutions for arbitrary quasi-periodic perturbations with Bryuno frequency vector
• Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
• Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems
• KAM theory in configuration space and cancellations in the Lindstedt series
• On the persistence of invariant curves for Fibered Holomorphic Transformations
• Invariant curves for exact symplectic twist maps of the cylinder with Bryuno rotation numbers