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Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

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Appendix D. Two or More Complex Variables

Let M be a complex manifold of dimension n ≥ 2, and let F : MM be a holomorphic map. As in the 1-dimensional case, we are interested in studying the behavior of the family of iterates Fok. Some of the constructions for the 1-dimensional case can be carried over to this higher dimensional case without essential change. However, there are many surprises and new difficulties.

Polynomial Maps. First consider the case of a nonlinear polynomial map

images

from the coordinate space imagen to itself. The Jacobian determinant ...

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