Dynamics of one-resonant biholomorphisms
Filippo Bracci
Università di Roma 'Tor Vergata', ItalyDmitri Zaitsev
Trinity College, Dublin, Ireland
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Abstract
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in whose differentials have one-dimensional family of resonances in the first eigenvalues, (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.
Cite this article
Filippo Bracci, Dmitri Zaitsev, Dynamics of one-resonant biholomorphisms. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 179–200
DOI 10.4171/JEMS/359