Road to holomorphic dynamics. What is the best route in order to learn holomorphic dynamics? I mean, suppose that I started with Strogatz's dynamical systems, then what is the next book that I have to read?

Try the books by Robert L. Devaney:


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*A First Course in Chaotic Dynamical Systems

*An Introduction to Chaotic Dynamical Systems
You may also try this survey:


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*P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bulletin of the American Mathematical Society, 11 (1984), 85–141


and this collection:


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*Robert L. Devaney and L. Keen (eds.), Chaos and Fractals: The Mathematics behind the Computer Graphics, Proceedings of Symposia in Applied Mathematics 39, AMS, 1989.

