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I desperately need to read the paper [1] before meeting a would-be supervisor, but with limited undergraduate knowledge that I have like Aluffi's Algebra and Churchill's Complex Analysis, not even one sentence of the paper is readable to me, so I even don't know what area of mathematics is it about!

What is the necessary prerequisite knowledge to be able to understand the mentioned paper and the best introductory books written about? Thank you!

[1]: Vincent Guedj, Nessim Sibony, Dynamics of polynomial automorphisms of $\mathbb C^k$, Arkiv för Matematik, Volume 40, Issue 2, (2002), pp 207–243. https://www.math.univ-toulouse.fr/~guedj/fichierspdf/Arkiv2002.pdf

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    $\begingroup$ Just a heads up! Try your best with the links given in the answers but if you still end up understanding basically nothing from the paper then be honest with the advisor. Sometimes professors completely forget what undergraduates do and don't know (in general) and set unrealistic tasks. In my experience from undergrad and grad days a certain amount of faking it is fine and expected but it won't benefit you to overdo it if you're totally lost. Good luck :) $\endgroup$
    – user108998
    Feb 16, 2019 at 18:50

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This paper is about holomorphic dynamics in high dimensions. I recommend to begin the study of holomorphic dynamics from the one-dimensional case, and the best book on the subject is J. Milnor, Dynamics in one complex variable, https://arxiv.org/abs/math/9201272. After that you may read the two survey articles mentioned in the first paragraph of the paper you want to read.

You may also need some background in pluripotential theory, the main technical tool in multidimensional dynamics theories.

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  • $\begingroup$ Essentially anything written by Milnor is worth reading. $\endgroup$
    – Todd Trimble ♦
    Feb 16, 2019 at 19:00
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    $\begingroup$ @Todd Trimble: I agree. But this book has an additional advantage that it is a very easy reading. $\endgroup$
    – Alexandre Eremenko
    Feb 16, 2019 at 19:29

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