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I am interested in reading about complex dynamics, Riemann surfaces, and related subjects, but I lack complex analysis as a prerequisite. I want a text that is rigorous and challenging (e.g. not a complex variables text focusing on computation), but nevertheless a good introduction to the subject. Ideally, being interested in some of the more geometric and topological sides of the subject, I would like something that has more of a topological flavor to it, e.g. assumes a knowledge of metric spaces and basic topology.

I considered Ahlfors, but I am skeptical as to whether this would actually be ideal for one's first exposure to the subject. Does anyone know of any other texts I could consider that would suit me?

As for my background, the most advanced analysis books I have read are Spivak's Calculus on Manifolds and the single-variable half of Rudin's Principles.

Thanks!

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    $\begingroup$ Lang's complex analysis book is pretty basic and would serve as a good introduction to the subject before moving on to something more advanced like Ahlfors. $\endgroup$ – user61527 May 25 '14 at 19:45
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    $\begingroup$ math.stackexchange.com/questions/789284/… $\endgroup$ – 2016 May 25 '14 at 19:51
  • $\begingroup$ @T.Bongers Thanks for the recommendation. I see that he includes a second part on geometric function theory, which is appealing. I'll consider this. $\endgroup$ – solstafir May 25 '14 at 19:53
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    $\begingroup$ Presumably you have already looked through the current literature on complex analytic dynamics, but what about an older review? Link: projecteuclid.org/download/pdf_1/euclid.bams/1183551835 , I thought this was fairly good and it leads you to what you need to know. Wikipedia also has translations of Fatou and Julia's original papers.Link: en.wikipedia.org/wiki/Gaston_Julia $\endgroup$ – Alan May 25 '14 at 21:14
  • $\begingroup$ I have read some expositions on the subject, but not any current research (or anything very advanced in general), as I figured I lacked the prerequisites (namely complex analysis). But I have recently become very interested in the subject, so I hope to be able to study some of the current literature soon in the future. Thanks for the link, though; I will bookmark it and try reading through it sometime soon. $\endgroup$ – solstafir May 25 '14 at 21:55

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