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Characteristic directions of two-dimensional biholomorphisms

  • Lorena López-Hernanz (a1) and Rudy Rosas (a2)

Abstract

We prove that for each characteristic direction $[v]$ of a tangent to the identity diffeomorphism of order $k+1$ in $(\mathbb{C}^{2},0)$ there exist either an analytic curve of fixed points tangent to $[v]$ or $k$ parabolic manifolds where all the orbits are tangent to $[v]$ , and that at least one of these parabolic manifolds is or contains a parabolic curve.

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The first author was partially supported by Ministerio de Economía y Competitividad, Spain, process MTM2016-77642-C2-1-P; the second author was supported by Vicerrectorado de Investigación de la Pontificia Universidad Católica del Perú.

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Characteristic directions of two-dimensional biholomorphisms

  • Lorena López-Hernanz (a1) and Rudy Rosas (a2)

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