04-320 A. Apte, R. de la Llave, N. Petrov

Regularity of critical circles in non-twist maps. (1462K, PS) Oct 10, 04

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Abstract. We study critical invariant circles of several noble rotation numbers at the edge of breakdown for area preserving maps of the cylinder which violate the twist conditions. These circles admit essentially unique parameterizations 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 show that, to the extent of the precision, it only depends on the tail of the continued fraction expansion.

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