Dynamics of one-resonant biholomorphisms

Filippo Bracci; Dmitri Zaitsev

Journal of the European Mathematical Society (2013)

  • Volume: 015, Issue: 1, page 179-200
  • ISSN: 1435-9855

Abstract

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Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C n 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.

How to cite

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Bracci, Filippo, and Zaitsev, Dmitri. "Dynamics of one-resonant biholomorphisms." Journal of the European Mathematical Society 015.1 (2013): 179-200. <http://eudml.org/doc/277457>.

@article{Bracci2013,
abstract = {Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in $C^n$ whose differentials have one-dimensional family of resonances in the first $m$ eigenvalues, $m\le n$ (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.},
author = {Bracci, Filippo, Zaitsev, Dmitri},
journal = {Journal of the European Mathematical Society},
keywords = {discrete dynamics; resonances; normal forms; basins of attraction; discrete dynamics; resonances; normal forms; basins of attraction},
language = {eng},
number = {1},
pages = {179-200},
publisher = {European Mathematical Society Publishing House},
title = {Dynamics of one-resonant biholomorphisms},
url = {http://eudml.org/doc/277457},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Bracci, Filippo
AU - Zaitsev, Dmitri
TI - Dynamics of one-resonant biholomorphisms
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 1
SP - 179
EP - 200
AB - Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in $C^n$ whose differentials have one-dimensional family of resonances in the first $m$ eigenvalues, $m\le n$ (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.
LA - eng
KW - discrete dynamics; resonances; normal forms; basins of attraction; discrete dynamics; resonances; normal forms; basins of attraction
UR - http://eudml.org/doc/277457
ER -

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