RT info:eu-repo/semantics/article
T1 Stable Manifolds of Two-dimensional Biholomorphisms Asymptotic to Formal Curves
A1 López-Hernanz, Lorena
A1 Raissy, Jasmin
A1 Ribón, Javier
A1 Sanz-Sánchez, Fernando
AB Let F ∈ Diff (C2, 0) be a germ of a holomorphic diffeomorphism and let G be aninvariant formal curve of F. Assume that the restricted diffeomorphism F|G is eitherhyperbolic attracting or rationally neutral non-periodic (these are the conditions thatthe diffeomorphism F|G should satisfy, if G were convergent, in order to have orbitsconverging to the origin). Then we prove that F has finitely many stable manifolds,either open domains or parabolic curves, consisting of and containing all convergingorbits asymptotic to G. Our results generalize to the case where G is a formal periodiccurve of F.
SN 1073-7928
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/68172
UL https://uvadoc.uva.es/handle/10324/68172
LA eng
NO International Mathematics Research Notices, Vol. 2021, No. 17, pp. 12847–12887
DS UVaDOC
RD 23-nov-2024