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- Title
ATTRACTING DOMAINS OF MAPS TANGENT TO THE IDENTITY WHOSE ONLY CHARACTERISTIC DIRECTION IS NON-DEGENERATE.
- Authors
LAPAN, SARA W.
- Abstract
Let f be a holomorphic germ on ℂ2 that fixes the origin and is tangent to the identity. Assume that f has a non-degenerate characteristic direction [v]. Hakim gave conditions that guarantee the existence of attracting domains along [v], however, when f has only one characteristic direction, these conditions are not satisfied. We prove that when [v] is unique, the existence results still hold. In particular, there is a domain Ω whose points converge to the origin along [v] and, on Ω, f is conjugate to a translation. Furthermore, if f is a global automorphism, the corresponding domain of attraction is a Fatou-Bieberbach domain.
- Subjects
MATHEMATICAL domains; MATHEMATICAL mappings; TANGENTS (Geometry); IDENTITIES (Mathematics); NON-degenerate perturbation theory; HOLOMORPHIC functions; MATHEMATICAL proofs
- Publication
International Journal of Mathematics, 2013, Vol 24, Issue 10, p-1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X13500833