Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C-n whose differentials have a 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.
Bracci, F., Zaitsev, D. (2013). Dynamics of one-resonant biholomorphisms. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 15(1), 179-200 [10.4171/JEMS/359].
Dynamics of one-resonant biholomorphisms
BRACCI, FILIPPO;
2013-01-01
Abstract
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C-n whose differentials have a 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.File in questo prodotto:
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