Geodesic
Dynamics of one-resonant biholomorphisms
Journal of the European Mathematical Society, Tome 15 (2013) no. 1, pp. 179-200

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Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in Cn 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.
DOI : 10.4171/jems/359
Classification : 35-XX, 32-XX, 00-XX
Keywords: Discrete dynamics, resonances, normal forms, basins of attraction 
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Filippo Bracci; Dmitri Zaitsev. Dynamics of one-resonant biholomorphisms. Journal of the European Mathematical Society, Tome 15 (2013) no. 1, pp. 179-200. doi: 10.4171/jems/359

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