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An application of the topological rigidity of the sine family. (English) Zbl 1161.37034

In [Ill. J. Math. 49, No. 4, 1171–1179 (2005; Zbl 1091.37016)], the author proved that for any bounded type of irrational number \(0<\theta<1,\) the boundary of the Siegel disk of \(e^{2\pi i\theta}\sin z\) is a quasi-circl passing through exactly two critical points \(\frac{\pi}2\) and \(-\frac{\pi}2.\) In this paper, the author gives a different proof for the same result.

MSC:

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Citations:

Zbl 1091.37016
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