### Abstract

In this paper we consider diffeomorphisms of ℂ^{2} of the special form F(z,w) = (w,-z + 2G(w)). For such maps the origin is a parabolic fixed point. Under certain hypotheses on G we prove the existence of a domain Ω ⊂ ℂ with 0 ∈ ∂Ω and of invariant complex curves w = f(z) and w = g(z), z ∈ Ω, for F^{-1} and F, such that F^{-n}(z,f(z)) → 0 and F^{n}(z,g(z)) → 0 as n → ∞.

Original language | English (US) |
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Pages (from-to) | 85-96 |

Number of pages | 12 |

Journal | Houston Journal of Mathematics |

Volume | 24 |

Issue number | 1 |

State | Published - Dec 1 1998 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Coman, D., & Dabija, M. (1998). On the dynamics of some diffeomorphisms of ℂ

^{2}near parabolic fixed points.*Houston Journal of Mathematics*,*24*(1), 85-96.