THE PARAMETER SPACE FOR COMPLEX CUBIC POLYNOMIALS

Publisher Summary This chapter discusses the parameter space for complex cubic polynomials. The dynamical behavior under iteration of a rational map is dominated by the behavior of the critical points. A rough partition of the parameter space can be based on the possible behaviors of the critical points. The main tools for understanding iteration of a monic polynomial P are the ϕ p -map and the h p -map: the ϕ p -map is defined in a neighborhood of ∞. The chapter describes dichotomy for dynamical behavior. Each copy of the Mandelbrot set corresponds to a Cantor set construction in the set of angles for rays. Cantor sets live in the dynamical planes and in the parameter space.