Contracting rigid germs in higher dimensions

Details Contracting rigid germs in higher dimensions Contracting rigid germs in higher dimensions

2011-09-30

arxiv.org/abs/1109.6803v1

Mathematics

Dynamical Systems

29 pages, 0 figures

Scientific paper

Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in arbitrary dimensions. Interestingly enough, we find new resonance phenomena involving the differential of f and its linear action on the fundamental group of the complement of the critical set.

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