Degenerate characteristic directions for maps tangent to the Identity

TL;DR

This paper extends the understanding of attracting basins for germs of holomorphic maps tangent to the identity in complex two-dimensional space, focusing on degenerate characteristic directions.

Contribution

It provides new conditions for the existence of basins along degenerate characteristic directions, complementing previous results for non-degenerate directions.

Findings

Established conditions for basins along degenerate directions

Extended Hakim's results to a broader class of characteristic directions

Contributed to the theory of local dynamics of holomorphic maps

Abstract

Let F be a germ of (C^2,O) tangent to the identity. Assume F has a characteristic direction [v]. In [Hak] Hakim gives conditions to guarantee the existence of an attracting basin to the origin along [v], in the case of [v] a non-degenerate characteristic direction. In this paper we give conditions to guarantee the existence of basins along [v] in the case of [v] a degenerate characteristic direction.