Someone could explain the concept of blow up used in holomorphic dynamics? Specifically in the context of iteration of holomorphics functions. This concept could be taken to some of the deformation spaces of a particular function? Bibliography is very welcomed.
2026-02-23 00:44:13.1771807453
Blow up in holomorphic dynamics
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Blow-ups are used in the construction of parabolic curves as described in Marco Abate's paper on diagonalisation of non-diagonalisable discrete holomorphic dynamical systems.
Brochero Martínez, Cano and López-Hernanz's paper gives a concise proof of existence in the $\mathbb C^2$-case.