Böttcher coordinates

Xavier Buff (1) , Adam Epstein (2) , Sarah Koch (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 WMI - Warwick Mathematics Institute
3 HARVARD - Department of Mathematics [Cambridge]

A well-known theorem of Böttcher asserts that an analytic germ f:(C,0)->(C,0) which has a superattracting fixed point at 0, more precisely of the form f(z) = az^k + o(z^k) for some a in C^*, is analytically conjugate to z->az^k by an analytic germ phi:(C,0)->(C,0) which is tangent to the identity at 0. In this article, we generalize this result to analytic maps of several complex variables.

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Xavier Buff, Adam Epstein, Sarah Koch. Böttcher coordinates. 2010. ⟨hal-00586042⟩