Taylor coefficients of the conformal map for the exterior of the reciprocal of the multibrot set. (English) Zbl 1455.37043
Summary: In this paper we investigate normalized conformal mappings of the exterior of the reciprocal of the Multibrot set and analyze the growth of the denominator of the coefficients. Our inequality improves Ewing and Schober’s result which was presented in [J. H. Ewing and G. Schober, J. Math. Anal. Appl. 170, No. 1, 104–114 (1992; Zbl 0766.30012)]. We use the coefficient formula of the author [in: Topics in finite or infinite dimensional complex analysis. Proceedings of the 19th international conference on finite or infinite dimensional complex analysis and applications (ICFIDCAA), Hiroshima, Japan, December 11–15, 2011. Sendai: Tohoku University Press. 237–248 (2013; Zbl 1333.37055)]. The straightforward adaptation of the proof in this paper slightly improves the main theorem of the author [Osaka J. Math. 52, No. 3, 737–746 (2015; Zbl 1352.37142)].
MSC:
| 37F46 | Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets |
| 30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
| 30C20 | Conformal mappings of special domains |
| 30C35 | General theory of conformal mappings |
References:
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