{"id":4,"date":"2017-08-30T15:35:17","date_gmt":"2017-08-30T18:35:17","guid":{"rendered":"http:\/\/www.professores.uff.br\/javier\/?page_id=4"},"modified":"2023-11-17T13:42:33","modified_gmt":"2023-11-17T16:42:33","slug":"research","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/javierribon\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<h5 style=\"text-align: center\">My areas of research are\u00a0dynamical systems, ordinary differential\u00a0equations, bifurcation theory, potential theory and<span class=\"Apple-converted-space\">\u00a0\u00a0<\/span>representations of groups both in the<span class=\"Apple-converted-space\">\u00a0 <\/span>local and the global settings.<\/h5>\n<h4 style=\"text-align: center\">Papers<\/h4>\n<ul>\n<li><a href=\"https:\/\/doi.org\/10.1016\/S0764-4442(01)01976-0\">Diff\u00e9omorphismes de (C2,0) tangents \u00e1 l&#8217;identit\u00e9 qui pr\u00e9servent la fibration de Hopf<\/a>. C.R. Acad. Sci. Paris S\u00e9r. I Math., v. 332, n.11, p. 1011-1014, 2001.<\/li>\n<li><a href=\"https:\/\/eudml.org\/doc\/84545\">Holomorphic extensions of formal objects<\/a>. Annalli Scuola Normale Superiore Pisa Classe Scienze, v. 3, n.4, p. 657-680, 2004.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1307\/mmj\/1123090765\">Families of diffeomorphismes without periodic curves<\/a>. The Michigan Mathematical Journal, v. 53, p. 243-256, 2005.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1017\/S0143385707000867\">Formal classification of unipotent parametrized diffeomorphisms<\/a>. Ergodic Theory &amp; Dynamical Systems (Print), v. 28, p. 1323-1365, 2008.<\/li>\n<li><a href=\"http:\/\/www.ams.org\/distribution\/mmj\/vol8-2-2008\/ribon.pdf\">Modulus of analytic classification for unfoldings of resonant diffeomorphisms<\/a>. Moscow Mathematical Journal (Online), v. 8, p. 1-77, 2008.<\/li>\n<li><a href=\"http:\/\/smf4.emath.fr\/en\/Publications\/Asterisque\/2009\/323\/html\/smf_ast_323_325-370.php\">Unfoldings of tangent to the identity diffeomorphisms<\/a>. Ast\u00e9risque, v. 323, p. 325-370, 2009.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.5802\/aif.2453\">Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy<\/a>. Annales de l&#8217;Institut Fourier, v. 59, p. 951-975, 2009.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1090\/S0065-9266-10-00590-9\">Topological classification of families of diffeomorphisms without small divisors<\/a>. Memoirs of the American Mathematical Society, v. 207, serie 975, 166 p., 2010.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1016\/j.jde.2012.09.009\">Embedding smooth and formal diffeomorphisms through the Jordan Chevalley decomposition<\/a>. Journal of Differential Equations (Print), v. 253, p. 3211-3231, 2012.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1007\/s00574-012-0012-4\">Extension of formal conjugations between diffeomorphisms<\/a>. Bulletin Brazilian Mathematical Society (Impresso), v. 43, p. 247-283, 2012.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1007\/s00209-014-1396-1\">Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem<\/a>. Mathematische Zeitschrift, v. 279, p. 849-877, 2014. Joint work with Jaime Velasco and Sebasti\u00e3o Firmo. <sup><br \/>\n<\/sup><\/li>\n<li><a href=\"https:\/\/doi.org\/10.1007\/s00208-013-0975-5\">Derived length of solvable groups of local diffeomorphisms<\/a>. Mathematische Annalen, v. 358, p. 701-728, 2014. Joint work with Mitchael Martelo.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1017\/etds.2014.58\">Fixed points of nilpotent actions on S2<\/a>. Ergodic Theory and Dynamical Systems, v. 36, p. 173-197, 2016.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1090\/proc\/13686\">Finite orbits for nilpotent actions on the torus<\/a>. Proceedings\u00a0 of the American Mathematical Society, v. 146, p. 195-208, 2017.\u00a0 Joint work with Sebasti\u00e3o Firmo.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1007\/s00209-016-1719-5\">Recurrent orbits of subgroups of local complex analytic diffeomorphisms<\/a>. Mathematische Zeitschrift, v. 285, p. 519-548, 2017.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1007\/s11856-018-1729-6\">Finite dimensional groups of local diffeomorphisms<\/a>. Israel Journal of Mathematics, v. 227, p. 289-329, 2018.<\/li>\n<li><a href=\"https:\/\/doi.org\/10.1515\/crelle-2016-0066\">The solvable length of groups of local diffeomorphisms<\/a>. Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal), v. 752, p. 105-139, 2019.<\/li>\n<li>Fixed points of nilpotent actions on R2. Ast\u00e9risque 415, 113-156 (2020). Joint work with\u00a0 Sebasti\u00e3o Firmo and Patrice Le Calvez.<\/li>\n<li><a href=\"https:\/\/aif.centre-mersenne.org\/item\/AIF_2019__69_3_993_0\/\">Topological rigidity of unfoldings of resonant diffeomorphisms<\/a>. Annales de l&#8217;Institut Fourier, v. 69, n. 3, p 993-1046, 2019.<\/li>\n<li><a href=\"https:\/\/www.cambridge.org\/core\/journals\/canadian-journal-of-mathematics\/article\/abs\/action-of-a-plane-singular-holomorphic-flow-on-a-noninvariant-branch\/12C90BC3B1193929B381DE9059CBE63B\">The action of a plane singular holomorphic flow on a non-invariant branch<\/a>. Joint work with Pedro Fortuny Ayuso. Canadian Journal of Mathematics, v. 72, n. 4, 835-866 (2020). DOI: <span class=\"text\">10.4153\/S0008414X19000221<\/span><\/li>\n<li><a href=\"https:\/\/www.cambridge.org\/core\/journals\/ergodic-theory-and-dynamical-systems\/article\/global-fixed-points-for-nilpotent-actions-on-the-torus\/8DD5FB40E2FC1B15576C0DCBA3F4C785\">Global fixed points for nilpotent actions on the torus<\/a>. Joint work with Sebasti\u00e3o Firmo. Ergodic Theory and Dynamical Systems, v. 40, n. 12, 3339-3367 (2020).<\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/1710.03728\">Stable manifolds of two-dimensional biholomorphisms asymptotic to formal curve<\/a>. Joint work with Lorena L\u00f3pez-Hernanz, Jasmin Raissy and Fernando Sanz-S\u00e1nchez. \u00a0<span style=\"font-size: inherit\">International Mathematics Research Notices, v. 2021, p. 12847-12887 (2021).<\/span><\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/2007.04757\">The local Poincar\u00e9 problem for irreducible branches<\/a>. Joint work with Jos\u00e9 Cano and Pedro Fortuny Ayuso. Revista Matematica Iberoamericana, v. 37, p. 2229-2244 (2020).<\/li>\n<li><a href=\"http:\/\/dx.doi.org\/10.1017\/S1474748020000717\">Boundness of intersection numbers for actions by two-dimensional biholomorphisms<\/a>. J. Inst. Math. Jussieu 21, No. 5, 1677-1700 (2022).<\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/1810.07244\">On the automorphism group of foliations with geometric transverse structure<\/a>. Joint work with Laurent Meersseman and Marcel Nicolau. Math. Z. 301, No. 2, 1603-1630 (2022).<\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/2002.07102v2\">Stable manifolds of biholomorphisms in C^n asymptotic to formal curves<\/a>. Joint work with Lorena L\u00f3pez-Hernanz, Fernando Sanz-S\u00e1nchez and Liz Vivas. Proc. Lond. Math. Soc. (3) 125, No. 2, 277-317 (2022).<\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/javierribon\/wp-content\/uploads\/sites\/118\/2023\/01\/fixed_point_curve_thmv2.pdf\">A fixed point curve theorem for finite orbits local diffeomorphisms<\/a>. Joint work with Lucivanio Lisboa. Ergodic Theory Dyn. Syst.<span>, <span class=\"text\">Volume 43 <\/span><\/span><span>, <span class=\"text\">Issue 12 <\/span><\/span><span>, December 2023<\/span> <span>, pp. 4138 &#8211; 4165<\/span><\/li>\n<li><em>Complexity of <\/em><span class=\"im\"><em>Puiseux solutions of differential and q-difference equations of order and degree one<\/em>. Joint work with Jos\u00e9 Cano and Pedro Fortuny Ayuso. Accepted for publication in Publicacions Matem\u00e0tiques.<\/span><\/li>\n<li><span class=\"im\"><em>The Poincar\u00e9 problem for <span class=\"il\">reducible<\/span> curves<\/em>. Joint work with Pedro Fortuny Ayuso. Accepted for publication in Revista Matematica Iberoamericana.<\/span><\/li>\n<\/ul>\n<h4 style=\"text-align: center\"><strong>Preprints<\/strong><\/h4>\n<ul>\n<li><a href=\"https:\/\/arxiv.org\/abs\/1009.3518\">Multisummability of unfoldings of tangent to the identity diffeomorphisms<\/a>.<\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/2101.04871\">Fixed points of nilpotent actions on surfaces of negative Euler characteristic.<\/a><\/li>\n<li><a href=\"https:\/\/doi.org\/10.48550\/arXiv.2301.09707\">Nondegenerate germs of holomorphic foliations with prescribed holonomy<\/a>. Joint work with Rudy Rosas.<\/li>\n<\/ul>\n<h4 style=\"text-align: center\"><strong>Chapters in books<\/strong><\/h4>\n<ul>\n<li><em>Algebraic properties of groups of complex analytic local diffeomorphisms<\/em>. In VIII Escuela Doctoral Intercontinental de Matem\u00e1ticas PUCP-UVA 2015. \u00a0Editors: Francisco Ugarte and Nuria Corral. Pontifica Universidad Cat\u00f3lica de Per\u00fa, 2015.<\/li>\n<li>\n<div>\n<div><em>Description of the Zariski-closure of a group of formal diffeomorphisms<\/em>. Accepted for publication in Handbook on Foliation Theory. Editors: Jos\u00e9 Seade and Felipe Cano. Springer.<\/div>\n<\/div>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>My areas of research are\u00a0dynamical systems, ordinary differential\u00a0equations, bifurcation theory, potential theory and\u00a0\u00a0representations of groups both in the\u00a0 local and the global settings. Papers Diff\u00e9omorphismes de (C2,0) tangents \u00e1 l&#8217;identit\u00e9 qui pr\u00e9servent la fibration de Hopf. C.R. Acad. Sci. Paris S\u00e9r. I Math., v. 332, n.11, p. 1011-1014, 2001. Holomorphic extensions of formal objects. Annalli [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-4","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/pages\/4","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/comments?post=4"}],"version-history":[{"count":63,"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/pages\/4\/revisions"}],"predecessor-version":[{"id":160,"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/pages\/4\/revisions\/160"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/media?parent=4"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/categories?post=4"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/javierribon\/wp-json\/wp\/v2\/tags?post=4"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}