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.
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Discrete dynamics; resonances; normal forms; basins of attraction
Bracci, F., Zaitsev, D. (2013). Dynamics of one-resonant biholomorphisms. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 15(1), 179-200 [10.4171/JEMS/359].
Bracci, F; Zaitsev, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/89912
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