The complex dynamics of quadratic polynomials. (English) Zbl 0820.58032

Devaney, Robert L.

Devaney, Robert L. (ed.), Complex dynamical systems. The mathematics behind the Mandelbrot and Julia sets. Lecture notes prepared for the American Mathematical Society short course, held in Cincinnati, OH, USA, January 10-11, 1994. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 49, 1-29 (1994).

According to the author the field of complex analytical dynamics has undergone rapid development after Mandelbrot used computer graphics to explore this field. This paper is to introduce the basic idea of complex analytical dynamics thus developed in the simplest possible setting, namely iteration of quadratic polynomials.
For the entire collection see [Zbl 0809.00024].

Reviewer: Y.Kozai (Tokyo)

MSC:

37B99	Topological dynamics
30D05	Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable

Keywords:

Mandelbrot set; complex analytical dynamics; iteration; quadratic polynomials