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  "body": "\n## Summary\n\nA Brjuno number is an [[irrational number|0DZXAXEJQ9]] whose [[continued fraction|04P2RJ4WPS]] convergents have denominators that do not grow too fast.\nThe condition is that the series $\\sum_n \\log(q_{n+1}) / q_n$ converges.\nBrjuno numbers are exactly the rotation numbers for which every holomorphic germ with that rotation at a fixed point can be linearized.\nThey are central to small divisor problems and to the existence of [[Siegel discs|KNDYA9T8ZK]].\n\n## Explanations\n\n### L1 human\n\nSome irrational numbers are very close to fractions with small denominators, and others stay away from all such fractions.\nA Brjuno number is one that is not approximated too well by fractions, measured in a precise, fairly generous way.\nThe golden mean is a Brjuno number, and in fact almost every real number is one.\nThe condition decides when a map that turns points near a fixed point by such an angle can be straightened into an exact rotation.\n",
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