Yin, Yongcheng Some dynamical properties of quadratic rational maps. (English) Zbl 0812.58069 Chin. Ann. Math., Ser. B 15, No. 3, 373-384 (1994). The author considers the dynamics of the analytic family of maps \(f_ b(z) = {z + 1 \over z + b}\). The topology of the parameter space is described and the structural and \(J\)-stability are investigated. If the Mandelbrot set \(\{b \mid J(f_ b)\) is connected} is denoted by \(M\) then it is shown that \(J(f_ b)\) has null measure for each \(b \in \mathbb{C} - M\). The mapping class groups are also described for almost all the maps of the family. Reviewer: R.Cowen (Nairobi) Cited in 1 Review MSC: 37F99 Dynamical systems over complex numbers 37B99 Topological dynamics 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable Keywords:quadratic rational maps; stability; parameter space; Mandelbrot set PDFBibTeX XMLCite \textit{Y. Yin}, Chin. Ann. Math., Ser. B 15, No. 3, 373--384 (1994; Zbl 0812.58069)