Dynamics of one-resonant biholomorphisms

Details Dynamics of one-resonant biholomorphisms Dynamics of one-resonant biholomorphisms

2009-12-02

arxiv.org/abs/0912.0428v2

Mathematics

Complex Variables

Final version, to appear in The Journal of the European Mathematical Society (JEMS)

Scientific paper

Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C^n whose differentials have one-dimensional family of resonances in the first m eigenvalues, m <= n (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions.

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