Analytic linearization of a generalization of the semi-standard map: radius of convergence and Brjuno sum

2021/06/25 by Chavaudret, Claire, Marmi, Stefano
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.13472

Abstract

One considers a system on ℂ² close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic linearization of the system around the invariant curve is bounded from below by exp(-(2)/(d)B(dα)-C), where C≥ 0 does not depend on α, d∈ ℕ^* and α is the frequency of the linear part. For a class of trigonometric polynomials, it is also bounded from above by a similar function. The error function is non decreasing with respect to the smallest coefficient of the trigonometric polynomial.

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