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.
Dynamics of one-resonant biholomorphisms / BRACCI, FILIPPO; Zaitsev, D.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 15:(2013), pp. 179-200. [10.4171/JEMS/359]
Dynamics of one-resonant biholomorphisms
BRACCI, FILIPPO;
2013
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.
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