Domain of attraction for maps tangent to the identity in ${\mathbb{C}}^2$ with characteristic direction of higher degree

Abstract

We study holomorphic fixed point germs in two complex variables that are tangent to the identity and have a degenerate characteristic direction. We show that if that characteristic direction is also a characteristic direction for higher degree terms, is non-degenerate for a higher degree term, and satisfies some additional properties, then there is a domain of attraction on which points converge to the origin along that direction.

arXiv commentWe modified two definitions, fixed minor typos, and added/extended a couple results. 17 pages, 1 table

References in corpus (3)

• Poincaré-Bendixson theorems for meromorphic connections and homogeneous vector fields
• Attracting domains of maps tangent to the identity whose only characteristic direction is non-degenerate
• Basins of attraction of automorphisms in C^3