Characteristic directions of two-dimensional biholomorphisms

López-Hernanz L.; Rosas R. · Compositio Mathematica (2020) · DOI: 10.1112/s0010437x20007071

Resumen

We prove that for each characteristic direction [v] of a tangent to the identity diffeomorphism of order k + 1 in (C2, 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. © Foundation Compositio Mathematica 2020.

Instituciones: Pontificia Universidad Católica del Perú