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This lecture explores the local dynamics of tangent to the identity biholomorphisms in C2, focusing specifically on the existence of invariant manifolds. Delve into the first results of existence of 1-dimensional invariant manifolds for tangent to the identity biholomorphisms obtained by Ecalle/Hakim and Abate, and understand how these connect to corresponding results for vector fields. The presentation is part of a three-lecture series delivered by Lorena López-Hernanz during the thematic meeting "Foliations, birational geometry and applications" at the Centre International de Rencontres Mathématiques (CIRM) in Marseille, France on February 4, 2024. Access this and other mathematical talks on CIRM's Audiovisual Mathematics Library, which offers features like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search functionality.
