Complex dynamics

Summary

Complex dynamics studies what happens when a holomorphic function is applied to its own output again and again. The main examples are rational functions on the Riemann sphere, polynomials on the plane and entire functions. The space splits into the Fatou set, where the behaviour is stable, and the Julia set, where it is chaotic. The subject joins complex analysis, topology and geometry, and it produced famous fractals such as the Mandelbrot set.