Scaling ratios and triangles in Siegel disks. (English) Zbl 0982.37037
This paper is devoted to determine a lower bound for the ratio of self-similarity. Let \(f(z)=e^{2\pi i\theta}z+z^2\), where \(\theta\) is a quadratic irrational. The authors show that if \(\theta=\frac{\sqrt 5-1}{2}\) is the golden mean, then there exists a triangle contained in the Siegel disk, and with one vertex at the critical point.
Reviewer: Messoud Efendiev (Berlin)
MSC:
37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
37F50 | Small divisors, rotation domains and linearization in holomorphic dynamics |