Dynamics of quadratic polynomials (Q2466999)

This paper is a very nice survey on holomorphic dynamics of rational maps, with particular aim to quadratic polynomials. The paper starts with a classification of periodic orbits. Then the authors discuss the local behavior around fixed and periodic points, going through the theorems of Königs, Böttcher, Siegel, Bruno and Yoccoz. Then they discuss the Fatou and the Julia sets and their properties. In particular they talk of nonwandering domains and Sullivan's result. Later sections are devoted to hyperbolicity and stability of mappings. Finally they specify to a quadratic family with Mandelbrot sets and renormalization. The authors wrote a really good state of arts on dynamics of quadratic polynomials that can be very useful as a good source for both experts and nonexperts in the area.