Regularity of critical invariant circles of the standard nontwist map

We study critical invariant circles of several noble rotation numbers at the edge of break-up for an area-preserving map of the cylinder, which violates the twist condition. These circles admit essentially unique parametrizations by rotational coordinates. We present a high accuracy computation of about 10 7 Fourier coefficients. This allows us to compute the regularity of the conjugating maps and to show that, to the extent of numerical precision, it only depends on the tail of the continued fraction expansion.