2026-04-26T07:15:50Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/681722024-12-04T07:43:54Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

Stable Manifolds of Two-dimensional Biholomorphisms Asymptotic to Formal Curves López Hernanz, Lorena Raissy, Jasmin Ribón, Javier Sanz Sánchez, Fernando Let F ∈ Diff (C2, 0) be a germ of a holomorphic diffeomorphism and let G be an invariant formal curve of F. Assume that the restricted diffeomorphism F|G is either hyperbolic attracting or rationally neutral non-periodic (these are the conditions that the diffeomorphism F|G should satisfy, if G were convergent, in order to have orbits converging to the origin). Then we prove that F has finitely many stable manifolds, either open domains or parabolic curves, consisting of and containing all converging orbits asymptotic to G. Our results generalize to the case where G is a formal periodic curve of F. 2024-06-21T08:54:40Z 2024-06-21T08:54:40Z 2021 info:eu-repo/semantics/article International Mathematics Research Notices, Vol. 2021, No. 17, pp. 12847–12887 1073-7928 https://uvadoc.uva.es/handle/10324/68172 10.1093/imrn/rnz143 12847 17 12887 International Mathematics Research Notices 2021 1687-0247 eng info:eu-repo/semantics/restrictedAccess SI