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López Hernanz, Lorena Raissy, Jasmin Ribón, Javier Sanz Sánchez, Fernando 2024-06-21T08:54:40Z 2024-06-21T08:54:40Z 2021 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 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. First, third and fourth authors partially supported by Ministerio de Economía y Competitividad, Spain, process MTM2016-77642-C2-1-P; first and second authors, by MATHAmSud 2014 grant “Geometry and Dynamics of Holomorphic Foliations”; second author, by ANR project LAMBDA, ANR-13-BS01-0002. application/pdf eng info:eu-repo/semantics/restrictedAccess Stable Manifolds of Two-dimensional Biholomorphisms Asymptotic to Formal Curves info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion SI