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One considers a system on $\mathbb{C}^2$ close to an invariant curve whichcan be viewed as a generalization of the semi-standard map to a trigonometricpolynomial with many Fourier modes. The radius of convergence of an analyticlinearization of the system around the invariant curve is bounded from below by$\exp(-\frac{2}{d}B(d\alpha)-C)$, where $C\geq 0$ does not depend on $\alpha$,$d\in \mathbb{N}^*$ and $\alpha$ is the frequency of the linear part. For aclass of trigonometric polynomials, it is also bounded from above by a similarfunction. The error function is non decreasing with respect to the smallestcoefficient of the trigonometric polynomial.

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