Dynamics of quasi-parabolic one-resonant biholomorphisms

Filippo Bracci; Feng Rong

Dynamics of quasi-parabolic one-resonant biholomorphisms

Complex Variables 2012-08-21 v2 Dynamical Systems

Authors: Filippo Bracci , Feng Rong

Abstract

In this paper we study the dynamics of germs of quasi-parabolic one-resonant biholomorphisms of $\C^{n+1}$ fixing the origin, namely, those germs whose differential at the origin has one eigenvalue 1 and the others having a one dimensional family of resonant relations. We define some invariants and give conditions which ensure the existence of attracting domains for such maps.

Keywords

quasi-parabolic biholomorphisms one-resonant dynamics attracting domains resonant relations germs complex dynamics

Cite

@article{arxiv.1208.1875,
  title  = {Dynamics of quasi-parabolic one-resonant biholomorphisms},
  author = {Filippo Bracci and Feng Rong},
  journal= {arXiv preprint arXiv:1208.1875},
  year   = {2012}
}

Comments

11 pages; some misprints corrected, a better explaination on the number of disjoint basins of attraction given

Dynamics of quasi-parabolic one-resonant biholomorphisms

Abstract

Keywords

Cite

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