Devaney, R. L.; Moreno Rocha, M. Geometry of the antennas in the Mandelbrot set. (English) Zbl 1072.37506 Fractals 10, No. 1, 39-46 (2002). Summary: In the Mandelbrot set, the bulbs attached directly to the main cardioid are called the p/q-bulbs. The reason for this is that the largest component of the interior of these bulbs consists of c-values for which the quadratic function \(Q_c(z) = z^2 + c\) admits an attracting cycle with rotation number p/q. We give a geometric method to read off p/q from the geometry of the antenna attached to the bulb. Cited in 1 ReviewCited in 6 Documents MSC: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010) 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets PDFBibTeX XMLCite \textit{R. L. Devaney} and \textit{M. Moreno Rocha}, Fractals 10, No. 1, 39--46 (2002; Zbl 1072.37506) Full Text: DOI References: [1] DOI: 10.2307/2589552 · Zbl 1076.37512 [2] LaVaurs P., C. R. Acad. Sci. Paris Sér. I Math. 303 pp 143– (1986) [3] Atela P., Ergod. Th. Dynam. Syst. 12 pp 401– (1991) [4] Douady A., Notes Rep. Math. Sci. Eng. 2 pp 155– (1986) [5] Farey J., Phil. Mag. J. London 47 pp 385– (1816) [6] DOI: 10.1142/S0218348X95000564 · Zbl 0929.37016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.