A. Apte, R. de la Llave, N. Petrov
Regularity of  critical circles in non-twist maps.
(1462K, PS)

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.