https://en.wikipedia.org/wiki/Complex_dynamics

http://www.math.harvard.edu/~ctm/papers/home/text/papers/real/book.pdf

Related to Fractals and Complex systems

Complex analytic dynamics on the Riemann sphere

Complex Dynamics: Families and Friends

Attracting Domain of a Dynamical System: A Complex Dance by Sara Lapan her webpage with some notes also on Algebraic geometry.