Abstract
This paper is concerned with the existence of Siegel disks of the Cremona map F?(x,y)=(x cos?-(y-x2) sin?, x sin?+(y-x2) cos?) with the parameter ? ? [0, 2?). This problem is reduced to the existence of local invertible analytic solutions to a functional equation with small divisors ?n + ?-n - ? - ?-1. The main aim of this paper is to investigate whether this equation with |?|=1 has such a solution under the Brjuno condition.
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