online-book: Milnor, dynamics in one complex variable
The book/lecture notes presents the key ideas of the modern dynamics in one complex variable (i.e. everything that has to do with iterations of holomorphic functions in the complex plane).

I found the chapter about local fixed point theory very interesting.
It presents our knowledge about Abel and Schröder functions in the light of complex dynamics.
Especially for parabolic fixed points, the Leau-Fatou-Flower explain this rather difficult case.

It applies for example to \( f(x)=e^{x/e} \), which has multiplicity 2 and hence one attracting and one repelling petal.

Its available for download here.

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