JournalsjemsVol. 15, No. 1pp. 179–200

Dynamics of one-resonant biholomorphisms

  • Dmitri Zaitsev

    Trinity College, Dublin, Ireland
  • Filippo Bracci

    Università di Roma 'Tor Vergata', Italy
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Abstract

Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in Cn\mathbb C^n whose differentials have one-dimensional family of resonances in the first mm eigenvalues, mnm\leq 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.

Cite this article

Dmitri Zaitsev, Filippo Bracci, Dynamics of one-resonant biholomorphisms. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 179–200

DOI 10.4171/JEMS/359