×

Some dynamical properties of quadratic rational maps. (English) Zbl 0812.58069

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)

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
PDFBibTeX XMLCite