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.