Edit Profile (opens in new tab) Dumortier, Freddy Co-Author Distance Author ID: dumortier.freddy Published as: Dumortier, Freddy; Dumortier, F. Homepage: https://www.uhasselt.be/fiche_en?voornaam=freddy&naam=dumortier External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 115 Publications since 1973, including 6 Books 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 45 Co-Authors with 102 Joint Publications 1,446 Co-Co-Authors all top 5 Co-Authors 15 single-authored 31 Roussarie, Robert 19 De Maesschalck, Peter 10 Li, Chengzhi 8 Caubergh, Magdalena 7 Rousseau, Christiane 6 Ibáñez, Santiago 5 Bonckaert, Patrick 5 Kaper, Tasso J. 5 Kokubu, Hiroshi 3 Luca, Stijn E. 3 Popović, Nikola 3 Sotomayor, Jorge 2 Artés, Joan Carles 2 Broer, Henk W. 2 Chicone, Carmen C. 2 Coll, Bartomeu 2 Fiddelaers, Peter 2 Gyssens, Marc 2 Herssens, Chris 2 Huzak, Renato 2 Llibre, Jaume 2 Prohens, Rafel 2 Takens, Floris 2 Van Gucht, Dirk 2 van Strien, Sebastian J. 2 Vandeurzen, Luc 1 Annabi, Mohamed Larbi 1 Bultheel, Adhemar François 1 de Melo, Welington 1 El Morsalani, Mohamed 1 Guzmán, Ana 1 Ilyashenko, Yulij Sergeevich 1 Kooij, Robert E. 1 Mawhin, Jean L. 1 Oka, Hiroe 1 Panazzolo, Daniel 1 Perko, Lawrence M. 1 Rodrigues, Paulo Roberto 1 Shafer, Douglas S. 1 Simó, Carles 1 Smits, Bert 1 Vanderbauwhede, Andre L. 1 Verduyn Lunel, Sjoerd M. 1 Zhang, Zifen 1 Żołądek, Henryk all top 5 Serials 31 Journal of Differential Equations 8 Nonlinearity 8 Discrete and Continuous Dynamical Systems 5 Ergodic Theory and Dynamical Systems 5 Qualitative Theory of Dynamical Systems 4 Proceedings of the American Mathematical Society 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Transactions of the American Mathematical Society 3 Communications on Pure and Applied Analysis 2 Annales de l’Institut Fourier 2 Boletim da Sociedade Brasileira de Matemática 2 Journal of Computer and System Sciences 2 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 2 Lecture Notes in Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Physica D 1 Publicacions Matemàtiques 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Dynamics and Differential Equations 1 Indagationes Mathematicae. New Series 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Annals of Mathematics. Second Series 1 Regular and Chaotic Dynamics 1 Dynamical Systems 1 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 1 Studies in Mathematical Physics 1 RIMS Kôkyûroku Bessatsu 1 Discrete and Continuous Dynamical Systems. Series S 1 Nonlinear Analysis. Theory, Methods & Applications 1 Universitext all top 5 Fields 82 Ordinary differential equations (34-XX) 53 Dynamical systems and ergodic theory (37-XX) 19 Global analysis, analysis on manifolds (58-XX) 7 Manifolds and cell complexes (57-XX) 6 Partial differential equations (35-XX) 4 General and overarching topics; collections (00-XX) 3 Computer science (68-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 103 Publications have been cited 2,878 times in 1,576 Documents Cited by ▼ Year ▼ Qualitative theory of planar differential systems. Zbl 1110.34002 Dumortier, Freddy; Llibre, Jaume; Artés, Joan C. 534 2006 Canard cycles and center manifolds. Zbl 0851.34057 Dumortier, Freddy; Roussarie, Robert 227 1996 Singularities of vector fields on the plane. Zbl 0346.58002 Dumortier, Freddy 137 1977 Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3. Zbl 0608.58034 Dumortier, F.; Roussarie, R.; Sotomayor, J. 102 1987 Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals. Zbl 0755.58002 Dumortier, F.; Roussarie, R.; Sotomayor, J.; Żoładek, H. 87 1991 Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations. Zbl 0791.58069 Dumortier, Freddy 81 1993 Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop. Zbl 1057.34015 Dumortier, Freddy; Li, Chengzhi 81 2003 Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles. Zbl 1004.34018 Dumortier, Freddy; Li, Chengzhi 72 2001 Hilbert’s 16th problem for quadratic vector fields. Zbl 0802.34028 Dumortier, F.; Roussarie, R.; Rousseau, C. 70 1994 Cubic Liénard equations with linear damping. Zbl 0716.58023 Dumortier, Freddy; Rousseau, Christiane 66 1990 Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop. Zbl 1034.34036 Dumortier, Freddy; Li, Chengzhi 63 2001 More limit cycles than expected in Liénard equations. Zbl 1130.34018 Dumortier, Freddy; Panazzolo, Daniel; Roussarie, Robert 58 2007 Perturbation from an elliptic Hamiltonian of degree four. III: global centre. Zbl 1056.34044 Dumortier, Freddy; Li, Chengzhi 52 2003 Time analysis and entry-exit relation near planar turning points. Zbl 1075.34048 De Maesschalck, P.; Dumortier, F. 51 2005 Multiple canard cycles in generalized Liénard equations. Zbl 1024.34038 Dumortier, Freddy; Roussarie, Robert 46 2001 Abelian integrals and limit cycles. Zbl 1111.34028 Dumortier, Freddy; Roussarie, Robert 38 2006 Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops. Zbl 0883.34035 Dumortier, Freddy; Li, Chengzhi; Zhang, Zifen 38 1997 On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations. Zbl 0907.58056 Dumortier, Freddy; Li, Chengzhi 37 1996 Cyclicity of common slow-fast cycles. Zbl 1233.34014 De Maesschalck, P.; Dumortier, F.; Roussarie, R. 37 2011 Elementary graphics of cyclicity 1 and 2. Zbl 0855.58043 Dumortier, F.; Roussarie, R.; Rousseau, C. 37 1994 Canard cycles in the presence of slow dynamics with singularities. Zbl 1263.37034 De Maesschalck, P.; Dumortier, F. 37 2008 Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}]+2\) limit cycles. Zbl 1215.37038 De Maesschalck, P.; Dumortier, F. 36 2011 Birth of canard cycles. Zbl 1186.34080 Dumortier, Freddy; Roussarie, Robert 35 2009 Quadratic Liénard equations with quadratic damping. Zbl 0881.34046 Dumortier, Freddy; Li, Chengzhi 34 1997 Bifurcations of cuspidal loops. Zbl 0908.58043 Dumortier, Freddy; Roussarie, Robert; Sotomayor, Jorge 32 1997 Canard solutions at non-generic turning points. Zbl 1086.34048 De Maesschalck, Peter; Dumortier, Freddy 31 2006 Polynomial Liénard equations near infinity. Zbl 0928.34028 Dumortier, Freddy; Herssens, Chris 30 1999 Finiteness for critical periods of planar analytic vector fields. Zbl 0773.34032 Chicone, Carmen; Dumortier, Freddy 30 1993 Germs of diffeomorphisms in the plane. Zbl 0502.58001 Dumortier, Freddy; Rodrigues, Paulo R.; Roussarie, Robert 28 1981 Hilbert’s 16th problem for quadratic systems and cyclicity of elementary graphics. Zbl 0895.58046 Dumortier, F.; El Morsalani, M.; Rousseau, C. 28 1996 Slow divergence integral and balanced canard solutions. Zbl 1215.34063 Dumortier, Freddy 26 2011 Structures in dynamics: finite dimensional deterministic studies. Zbl 0746.58002 Broer, H. W.; Dumortier, F.; van Strien, S. J.; Takens, F. 26 1991 Compactification and desingularization of spaces of polynomial Liénard equations. Zbl 1105.34015 Dumortier, Freddy 25 2006 About the unfolding of a Hopf-zero singularity. Zbl 1283.34039 Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi; Simó, Carles 25 2013 Slow-fast Bogdanov-Takens bifurcations. Zbl 1236.34083 De Maesschalck, P.; Dumortier, F. 23 2011 New aspects in the unfolding of the nilpotent singularity of codimension three. Zbl 0993.37026 Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi 22 2001 Geometric singular perturbation theory beyond normal hyperbolicity. Zbl 1007.34058 Dumortier, Freddy; Roussarie, Robert 21 2001 Cocoon bifurcation in three-dimensional reversible vector fields. Zbl 1107.34039 Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi 20 2006 The critical wave speed for the Fisher-Kolmogorov-Petrowskii-Piscounov equation with cut-off. Zbl 1139.35056 Dumortier, Freddy; Popović, Nikola; Kaper, Tasso J. 19 2007 The period function of classical Liénard equations. Zbl 1121.34046 De Maesschalck, P.; Dumortier, F. 17 2007 Hilbert’s 16th problem for classical Liénard equations of even degree. Zbl 1146.34028 Caubergh, M.; Dumortier, F. 17 2008 A quadratic system with a nonmonotonic period function. Zbl 0651.34043 Chicone, Carmen; Dumortier, Freddy 16 1988 Singular perturbations and vanishing passage through a turning point. Zbl 1277.34081 de Maesschalck, P.; Dumortier, F. 16 2010 Hopf-Takens bifurcations and centres. Zbl 1059.34026 Caubergh, M.; Dumortier, F. 16 2004 Singularities of vector fields on \(\mathbb{R}^3\). Zbl 0907.58051 Dumortier, F.; Ibáñez, S. 15 1998 Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields. Zbl 0865.58032 Dumortier, F.; Ibáñez, S. 15 1996 Canard cycles with two breaking parameters. Zbl 1140.34019 Dumortier, Freddy; Roussarie, Robert 14 2007 Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations. Zbl 1316.34060 Huzak, R.; De Maesschalck, P.; Dumortier, F. 14 2013 Local bifurcations and a survey of bounded quadratic systems. Zbl 0961.34029 Dumortier, Freddy; Herssens, Chris; Perko, Lawrence 13 2000 Quadratic models for generic local 3-parameter bifurcation on the plane. Zbl 0737.58039 Dumortier, Freddy; Fiddelaers, Peter 13 1991 A degenerate singularity generating geometric Lorenz attractors. Zbl 0836.58030 Dumortier, Freddy; Kokubu, Hiroshi; Oka, Hiroe 12 1995 Canard cycle transition at a slow-fast passage through a jump point. (Transition de cycles canard pour un passage lent-rapide par un point de saut.) Zbl 1291.34097 De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert 12 2014 Canard cycles. From birth to transition. Zbl 1515.34002 De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert 11 2022 Singularities of vector fields on \({\mathbb{R}}^ 3\) determined by their first non-vanishing jet. Zbl 0661.58005 Bonckaert, Patrick; Dumortier, Freddy; Van Strien, Sebastian 10 1989 Detectable canard cycles with singular slow dynamics of any order at the turning point. Zbl 1235.34170 De Maesschalck, P.; Dumortier, Freddy 10 2011 Alien limit cycles near a Hamiltonian 2-saddle cycle. Zbl 1083.34025 Caubergh, Magdalena; Dumortier, Freddy; Roussarie, Robert 10 2005 Bifurcations of multiple relaxation oscillations in polynomial Liénard equations. Zbl 1230.37061 De Maesschalck, P.; Dumortier, F. 10 2011 Alien limit cycles in Liénard equations. Zbl 1262.34036 Coll, B.; Dumortier, F.; Prohens, R. 10 2013 Generic unfolding of the nilpotent saddle of codimension four. Zbl 1198.37081 Dumortier, Freddy; Fiddelaers, Peter; Li, Chengzhi 9 2001 Smooth linearization of germs of \(\mathbb{R}^2\)-actions and holomorphic vector fields. Zbl 0418.58015 Dumortier, F.; Roussarie, R. 9 1980 Bifurcation of relaxation oscillations in dimension two. Zbl 1157.34037 Dumortier, Freddy; Roussairie, Robert 9 2007 Canard-cycle transition at a fast-fast passage through a jump point. (Transition de cycles canard pour un passage rapide-rapide par un point de saut.) Zbl 1287.34044 De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert 8 2014 Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle. Zbl 1138.34020 Caubergh, Magdalena; Dumortier, Freddy; Roussarie, Robert 7 2007 The asymptotic critical wave speed in a family of scalar reaction-diffusion equations. Zbl 1110.35025 Dumortier, Freddy; Popović, Nikola; Kaper, Tasso J. 7 2007 Chaotic dynamics in \(\mathbb{Z}_2\)-equivariant unfoldings of codimension three singularities of vector fields in \(\mathbb{R}^3\). Zbl 0944.37015 Dumortier, Freddy; Kokubu, Hiroshi 7 2000 Cubic Liénard equations with quadratic damping having two antisaddles. Zbl 1025.34029 Dumortier, Freddy; Kooij, Robert E.; Li, Chengzhi 7 2000 Smooth invariant curves for germs of vector fields in \({\mathbb{R}}^ 3\) whose linear part generates a rotation. Zbl 0584.58009 Bonckaert, Patrick; Dumortier, Freddy 7 1986 Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations. Zbl 1322.34067 Huzak, Renato; De Maesschalck, P.; Dumortier, Freddy 7 2014 A geometric approach to bistable front propagation in scalar reaction-diffusion equations with cut-off. Zbl 1206.35144 Dumortier, Freddy; Popović, Nikola; Kaper, Tasso J. 7 2010 Multi-layer canard cycles and translated power functions. Zbl 1355.34055 Dumortier, Freddy; Roussarie, Robert 6 2008 Limit cycles near hyperbolas in quadratic systems. Zbl 1169.34030 Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume 6 2009 A type of moduli for saddle connections of planar diffeomorphisms. Zbl 0672.58036 De Melo, W.; Dumortier, F. 5 1988 Detecting alien limit cycles near a Hamiltonian 2-saddle cycle. Zbl 1194.34084 Luca, Stijn; Dumortier, Freddy; Caubergh, Magdalena; Roussarie, Robert 5 2009 Study of the cyclicity of some degenerate graphics inside quadratic systems. Zbl 1170.34020 Dumortier, Freddy; Rousseau, Christiane 5 2009 Normal forms near a saddle-node and applications to finite cyclicity of graphics. Zbl 1013.37044 Dumortier, F.; Ilyashenko, Y.; Rousseau, C. 5 2002 Configurations of limit cycles in Liénard equations. Zbl 1297.34043 Coll, B.; Dumortier, F.; Prohens, R. 5 2013 Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilite finie. Zbl 0488.58005 Dumortier, F.; Roussarie, R. 4 1983 On a linearization theorem of Sternberg for germs of diffeomorphisms. Zbl 0506.57018 Bonckaert, Patrick; Dumortier, Freddy 4 1984 On the decidability of semilinearity for semialgebraic sets and its implications for spatial databases. Zbl 0939.68027 Dumortier, Freddy; Gyssens, Marc; Vandeurzen, Luc; Van Gucht, Dirk 4 1999 Sharp upperbounds for the number of large amplitude limit cycles in polynomial Liénard systems. Zbl 1277.34037 Dumortier, Freddy 4 2012 Algebraic curves of maximal cyclicity. Zbl 1330.34049 Caubergh, Magdalena; Dumortier, Freddy 4 2006 Wave speeds for the FKPP equation with enhancements of the reaction function. Zbl 1479.35190 Dumortier, Freddy; Kaper, Tasso J. 4 2015 Smooth normal linearization of vector fields near lines of singularities. Zbl 1221.34104 Dumortier, Freddy; Roussarie, Robert 4 2010 Restrictions on the equivalence homeomorphism in stability of polynomial vector fields. Zbl 0664.58021 Dumortier, Freddy; Shafer, Douglas S. 3 1990 Well adapted normal linearization in singular perturbation problems. Zbl 1215.34042 Bonckaert, P.; De Maesschalck, P.; Dumortier, F. 3 2011 On the saddle loop bifurcation. Zbl 0731.34010 Dumortier, F.; Roussarie, R. 3 1990 Non-stabilisable jets of diffeomorphisms in \({\mathbb{R}}^ 2\) and of vector fields in \({\mathbb{R}}^ 3\). Zbl 0628.58037 Dumortier, Freddy 2 1986 Cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Liénard systems. Zbl 1200.34034 Caubergh, Magdalena; Dumortier, Freddy; Luca, Stijn 2 2010 Transition time analysis in singularly perturbed boundary value problems. Zbl 0849.34019 Dumortier, Freddy; Smits, Bert 2 1995 Codimension 4 singularities of reflectionally symmetric planar vector fields. Zbl 0964.58034 Dumortier, F.; Ibáñez, S. 2 1999 Time and entry-exit relation near a planar turning point. Zbl 1082.34046 De Maesschalck, Peter; Dumortier, Freddy 2 2004 Singularités de champs de vecteurs sur le plan germes déterminés par un jet d’ordre fini. Zbl 0294.58005 Dumortier, Freddy 2 1974 Asymptotic phase and invariant foliations near periodic orbits. Zbl 1103.34039 Dumortier, Freddy 2 2006 Linearisation différentiable des germes singuliers d’actions de \(R^2\) et de champs de vecteurs holomorphes. Zbl 0367.58003 Dumortier, Freddy; Roussarie, Robert 2 1977 Characterization of compactness for symplectic manifolds. Zbl 0378.58004 Dumortier, F.; Takens, F. 2 1973 Wave speeds for pushed fronts in reaction-diffusion equations with cut-offs. Zbl 1258.35119 Dumortier, Freddy; Kaper, Tasso J. 2 2012 Smooth invariant curves for germs of vector fields in \({\mathbb{R}}^ 3\) whose linear part generates a rotation. Zbl 0537.58011 Bonckaert, Patrick; Dumortier, Freddy 1 1985 Corrigendum to: “On the decidability of semilinearity for semialgebraic sets and its implications for spatial databases. Zbl 0946.68035 Dumortier, Freddy; Gyssens, Marc; Vandeurzen, Luc; Van Gucht, Dirk 1 1999 Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. Zbl 1042.34062 Dumortier, F.; Guzmán, A.; Rousseau, C. 1 2002 Continuous dependence on parameters in the Bogdanov-Takens bifurcation. Zbl 0766.58038 Annabi, H.; Annabi, M. L.; Dumortier, F. 1 1992 Canard cycles. From birth to transition. Zbl 1515.34002 De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert 11 2022 Wave speeds for the FKPP equation with enhancements of the reaction function. Zbl 1479.35190 Dumortier, Freddy; Kaper, Tasso J. 4 2015 Canard cycle transition at a slow-fast passage through a jump point. (Transition de cycles canard pour un passage lent-rapide par un point de saut.) Zbl 1291.34097 De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert 12 2014 Canard-cycle transition at a fast-fast passage through a jump point. (Transition de cycles canard pour un passage rapide-rapide par un point de saut.) Zbl 1287.34044 De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert 8 2014 Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations. Zbl 1322.34067 Huzak, Renato; De Maesschalck, P.; Dumortier, Freddy 7 2014 About the unfolding of a Hopf-zero singularity. Zbl 1283.34039 Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi; Simó, Carles 25 2013 Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations. Zbl 1316.34060 Huzak, R.; De Maesschalck, P.; Dumortier, F. 14 2013 Alien limit cycles in Liénard equations. Zbl 1262.34036 Coll, B.; Dumortier, F.; Prohens, R. 10 2013 Configurations of limit cycles in Liénard equations. Zbl 1297.34043 Coll, B.; Dumortier, F.; Prohens, R. 5 2013 Canard explosion and position curves. Zbl 1314.37036 Dumortier, Freddy 1 2013 Sharp upperbounds for the number of large amplitude limit cycles in polynomial Liénard systems. Zbl 1277.34037 Dumortier, Freddy 4 2012 Wave speeds for pushed fronts in reaction-diffusion equations with cut-offs. Zbl 1258.35119 Dumortier, Freddy; Kaper, Tasso J. 2 2012 Cyclicity of common slow-fast cycles. Zbl 1233.34014 De Maesschalck, P.; Dumortier, F.; Roussarie, R. 37 2011 Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}]+2\) limit cycles. Zbl 1215.37038 De Maesschalck, P.; Dumortier, F. 36 2011 Slow divergence integral and balanced canard solutions. Zbl 1215.34063 Dumortier, Freddy 26 2011 Slow-fast Bogdanov-Takens bifurcations. Zbl 1236.34083 De Maesschalck, P.; Dumortier, F. 23 2011 Detectable canard cycles with singular slow dynamics of any order at the turning point. Zbl 1235.34170 De Maesschalck, P.; Dumortier, Freddy 10 2011 Bifurcations of multiple relaxation oscillations in polynomial Liénard equations. Zbl 1230.37061 De Maesschalck, P.; Dumortier, F. 10 2011 Well adapted normal linearization in singular perturbation problems. Zbl 1215.34042 Bonckaert, P.; De Maesschalck, P.; Dumortier, F. 3 2011 Singular perturbations and vanishing passage through a turning point. Zbl 1277.34081 de Maesschalck, P.; Dumortier, F. 16 2010 A geometric approach to bistable front propagation in scalar reaction-diffusion equations with cut-off. Zbl 1206.35144 Dumortier, Freddy; Popović, Nikola; Kaper, Tasso J. 7 2010 Smooth normal linearization of vector fields near lines of singularities. Zbl 1221.34104 Dumortier, Freddy; Roussarie, Robert 4 2010 Cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Liénard systems. Zbl 1200.34034 Caubergh, Magdalena; Dumortier, Freddy; Luca, Stijn 2 2010 Birth of canard cycles. Zbl 1186.34080 Dumortier, Freddy; Roussarie, Robert 35 2009 Limit cycles near hyperbolas in quadratic systems. Zbl 1169.34030 Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume 6 2009 Detecting alien limit cycles near a Hamiltonian 2-saddle cycle. Zbl 1194.34084 Luca, Stijn; Dumortier, Freddy; Caubergh, Magdalena; Roussarie, Robert 5 2009 Study of the cyclicity of some degenerate graphics inside quadratic systems. Zbl 1170.34020 Dumortier, Freddy; Rousseau, Christiane 5 2009 Book review of: Colin Christopher and Chengzhi Li, Limit cycles of differential equations. Zbl 1292.00022 Dumortier, Freddy 1 2009 Canard cycles in the presence of slow dynamics with singularities. Zbl 1263.37034 De Maesschalck, P.; Dumortier, F. 37 2008 Hilbert’s 16th problem for classical Liénard equations of even degree. Zbl 1146.34028 Caubergh, M.; Dumortier, F. 17 2008 Multi-layer canard cycles and translated power functions. Zbl 1355.34055 Dumortier, Freddy; Roussarie, Robert 6 2008 More limit cycles than expected in Liénard equations. Zbl 1130.34018 Dumortier, Freddy; Panazzolo, Daniel; Roussarie, Robert 58 2007 The critical wave speed for the Fisher-Kolmogorov-Petrowskii-Piscounov equation with cut-off. Zbl 1139.35056 Dumortier, Freddy; Popović, Nikola; Kaper, Tasso J. 19 2007 The period function of classical Liénard equations. Zbl 1121.34046 De Maesschalck, P.; Dumortier, F. 17 2007 Canard cycles with two breaking parameters. Zbl 1140.34019 Dumortier, Freddy; Roussarie, Robert 14 2007 Bifurcation of relaxation oscillations in dimension two. Zbl 1157.34037 Dumortier, Freddy; Roussairie, Robert 9 2007 Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle. Zbl 1138.34020 Caubergh, Magdalena; Dumortier, Freddy; Roussarie, Robert 7 2007 The asymptotic critical wave speed in a family of scalar reaction-diffusion equations. Zbl 1110.35025 Dumortier, Freddy; Popović, Nikola; Kaper, Tasso J. 7 2007 Qualitative theory of planar differential systems. Zbl 1110.34002 Dumortier, Freddy; Llibre, Jaume; Artés, Joan C. 534 2006 Abelian integrals and limit cycles. Zbl 1111.34028 Dumortier, Freddy; Roussarie, Robert 38 2006 Canard solutions at non-generic turning points. Zbl 1086.34048 De Maesschalck, Peter; Dumortier, Freddy 31 2006 Compactification and desingularization of spaces of polynomial Liénard equations. Zbl 1105.34015 Dumortier, Freddy 25 2006 Cocoon bifurcation in three-dimensional reversible vector fields. Zbl 1107.34039 Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi 20 2006 Algebraic curves of maximal cyclicity. Zbl 1330.34049 Caubergh, Magdalena; Dumortier, Freddy 4 2006 Asymptotic phase and invariant foliations near periodic orbits. Zbl 1103.34039 Dumortier, Freddy 2 2006 Time analysis and entry-exit relation near planar turning points. Zbl 1075.34048 De Maesschalck, P.; Dumortier, F. 51 2005 Alien limit cycles near a Hamiltonian 2-saddle cycle. Zbl 1083.34025 Caubergh, Magdalena; Dumortier, Freddy; Roussarie, Robert 10 2005 Hopf-Takens bifurcations and centres. Zbl 1059.34026 Caubergh, M.; Dumortier, F. 16 2004 Time and entry-exit relation near a planar turning point. Zbl 1082.34046 De Maesschalck, Peter; Dumortier, Freddy 2 2004 Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop. Zbl 1057.34015 Dumortier, Freddy; Li, Chengzhi 81 2003 Perturbation from an elliptic Hamiltonian of degree four. III: global centre. Zbl 1056.34044 Dumortier, Freddy; Li, Chengzhi 52 2003 Normal forms near a saddle-node and applications to finite cyclicity of graphics. Zbl 1013.37044 Dumortier, F.; Ilyashenko, Y.; Rousseau, C. 5 2002 Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. Zbl 1042.34062 Dumortier, F.; Guzmán, A.; Rousseau, C. 1 2002 Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles. Zbl 1004.34018 Dumortier, Freddy; Li, Chengzhi 72 2001 Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop. Zbl 1034.34036 Dumortier, Freddy; Li, Chengzhi 63 2001 Multiple canard cycles in generalized Liénard equations. Zbl 1024.34038 Dumortier, Freddy; Roussarie, Robert 46 2001 New aspects in the unfolding of the nilpotent singularity of codimension three. Zbl 0993.37026 Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi 22 2001 Geometric singular perturbation theory beyond normal hyperbolicity. Zbl 1007.34058 Dumortier, Freddy; Roussarie, Robert 21 2001 Generic unfolding of the nilpotent saddle of codimension four. Zbl 1198.37081 Dumortier, Freddy; Fiddelaers, Peter; Li, Chengzhi 9 2001 Local bifurcations and a survey of bounded quadratic systems. Zbl 0961.34029 Dumortier, Freddy; Herssens, Chris; Perko, Lawrence 13 2000 Chaotic dynamics in \(\mathbb{Z}_2\)-equivariant unfoldings of codimension three singularities of vector fields in \(\mathbb{R}^3\). Zbl 0944.37015 Dumortier, Freddy; Kokubu, Hiroshi 7 2000 Cubic Liénard equations with quadratic damping having two antisaddles. Zbl 1025.34029 Dumortier, Freddy; Kooij, Robert E.; Li, Chengzhi 7 2000 Polynomial Liénard equations near infinity. Zbl 0928.34028 Dumortier, Freddy; Herssens, Chris 30 1999 On the decidability of semilinearity for semialgebraic sets and its implications for spatial databases. Zbl 0939.68027 Dumortier, Freddy; Gyssens, Marc; Vandeurzen, Luc; Van Gucht, Dirk 4 1999 Codimension 4 singularities of reflectionally symmetric planar vector fields. Zbl 0964.58034 Dumortier, F.; Ibáñez, S. 2 1999 Corrigendum to: “On the decidability of semilinearity for semialgebraic sets and its implications for spatial databases. Zbl 0946.68035 Dumortier, Freddy; Gyssens, Marc; Vandeurzen, Luc; Van Gucht, Dirk 1 1999 Singularities of vector fields on \(\mathbb{R}^3\). Zbl 0907.58051 Dumortier, F.; Ibáñez, S. 15 1998 Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops. Zbl 0883.34035 Dumortier, Freddy; Li, Chengzhi; Zhang, Zifen 38 1997 Quadratic Liénard equations with quadratic damping. Zbl 0881.34046 Dumortier, Freddy; Li, Chengzhi 34 1997 Bifurcations of cuspidal loops. Zbl 0908.58043 Dumortier, Freddy; Roussarie, Robert; Sotomayor, Jorge 32 1997 Canard cycles and center manifolds. Zbl 0851.34057 Dumortier, Freddy; Roussarie, Robert 227 1996 On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations. Zbl 0907.58056 Dumortier, Freddy; Li, Chengzhi 37 1996 Hilbert’s 16th problem for quadratic systems and cyclicity of elementary graphics. Zbl 0895.58046 Dumortier, F.; El Morsalani, M.; Rousseau, C. 28 1996 Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields. Zbl 0865.58032 Dumortier, F.; Ibáñez, S. 15 1996 A degenerate singularity generating geometric Lorenz attractors. Zbl 0836.58030 Dumortier, Freddy; Kokubu, Hiroshi; Oka, Hiroe 12 1995 Transition time analysis in singularly perturbed boundary value problems. Zbl 0849.34019 Dumortier, Freddy; Smits, Bert 2 1995 Hilbert’s 16th problem for quadratic vector fields. Zbl 0802.34028 Dumortier, F.; Roussarie, R.; Rousseau, C. 70 1994 Elementary graphics of cyclicity 1 and 2. Zbl 0855.58043 Dumortier, F.; Roussarie, R.; Rousseau, C. 37 1994 Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations. Zbl 0791.58069 Dumortier, Freddy 81 1993 Finiteness for critical periods of planar analytic vector fields. Zbl 0773.34032 Chicone, Carmen; Dumortier, Freddy 30 1993 Continuous dependence on parameters in the Bogdanov-Takens bifurcation. Zbl 0766.58038 Annabi, H.; Annabi, M. L.; Dumortier, F. 1 1992 Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals. Zbl 0755.58002 Dumortier, F.; Roussarie, R.; Sotomayor, J.; Żoładek, H. 87 1991 Structures in dynamics: finite dimensional deterministic studies. Zbl 0746.58002 Broer, H. W.; Dumortier, F.; van Strien, S. J.; Takens, F. 26 1991 Quadratic models for generic local 3-parameter bifurcation on the plane. Zbl 0737.58039 Dumortier, Freddy; Fiddelaers, Peter 13 1991 Cubic Liénard equations with linear damping. Zbl 0716.58023 Dumortier, Freddy; Rousseau, Christiane 66 1990 Restrictions on the equivalence homeomorphism in stability of polynomial vector fields. Zbl 0664.58021 Dumortier, Freddy; Shafer, Douglas S. 3 1990 On the saddle loop bifurcation. Zbl 0731.34010 Dumortier, F.; Roussarie, R. 3 1990 Singularities of vector fields on \({\mathbb{R}}^ 3\) determined by their first non-vanishing jet. Zbl 0661.58005 Bonckaert, Patrick; Dumortier, Freddy; Van Strien, Sebastian 10 1989 A quadratic system with a nonmonotonic period function. Zbl 0651.34043 Chicone, Carmen; Dumortier, Freddy 16 1988 A type of moduli for saddle connections of planar diffeomorphisms. Zbl 0672.58036 De Melo, W.; Dumortier, F. 5 1988 Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3. Zbl 0608.58034 Dumortier, F.; Roussarie, R.; Sotomayor, J. 102 1987 Smooth invariant curves for germs of vector fields in \({\mathbb{R}}^ 3\) whose linear part generates a rotation. Zbl 0584.58009 Bonckaert, Patrick; Dumortier, Freddy 7 1986 Non-stabilisable jets of diffeomorphisms in \({\mathbb{R}}^ 2\) and of vector fields in \({\mathbb{R}}^ 3\). Zbl 0628.58037 Dumortier, Freddy 2 1986 Smooth invariant curves for germs of vector fields in \({\mathbb{R}}^ 3\) whose linear part generates a rotation. Zbl 0537.58011 Bonckaert, Patrick; Dumortier, Freddy 1 1985 On a linearization theorem of Sternberg for germs of diffeomorphisms. Zbl 0506.57018 Bonckaert, Patrick; Dumortier, Freddy 4 1984 Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilite finie. Zbl 0488.58005 Dumortier, F.; Roussarie, R. 4 1983 Germs of diffeomorphisms in the plane. Zbl 0502.58001 Dumortier, Freddy; Rodrigues, Paulo R.; Roussarie, Robert 28 1981 Smooth linearization of germs of \(\mathbb{R}^2\)-actions and holomorphic vector fields. Zbl 0418.58015 Dumortier, F.; Roussarie, R. 9 1980 Singularities of vector fields on the plane. Zbl 0346.58002 Dumortier, Freddy 137 1977 Linearisation différentiable des germes singuliers d’actions de \(R^2\) et de champs de vecteurs holomorphes. Zbl 0367.58003 Dumortier, Freddy; Roussarie, Robert 2 1977 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,322 Authors 209 Llibre, Jaume 81 Valls Anglés, Cláudia 53 Dumortier, Freddy 39 Han, Maoan 39 Zhang, Xiang 38 Giné, Jaume 37 De Maesschalck, Peter 35 Chen, Hebai 33 Gasull, Armengol 30 Zhao, Yulin 29 Li, Chengzhi 26 Roussarie, Robert 25 Algaba, Antonio 25 Torregrosa, Joan 24 Huzak, Renato 24 Oliveira, Regilene D. S. 22 Kühn, Christian 20 Tang, Yilei 20 Uldall Kristiansen, K. 19 González-Olivares, Eduardo 19 Liu, Changjian 19 Teixeira, Marco Antonio 18 Rojas-Palma, Alejandro 18 Wechselberger, Martin 18 Xiao, Dongmei 17 Li, Shimin 17 Szmolyan, Peter 16 Buzzi, Claudio Aguinaldo 16 Huang, Jicai 16 Rodríguez-Luis, Alejandro J. 15 Da Silva, Paulo Ricardo 14 Artés, Joan Carles 14 Sun, Xianbo 14 Zhu, Huaiping 13 Chen, Xingwu 13 Popović, Nikola 13 Yu, Pei 13 Zhao, Liqin 12 Villadelprat, Jordi 12 Zhang, Weinian 11 Desroches, Mathieu 11 Ferragut, Antoni 11 García, Cristóbal 11 Rousseau, Christiane 11 Schlomiuk, Dana I. 11 Yang, Junmin 10 Asheghi, Rasoul 10 Bonckaert, Patrick 10 García, Isaac A. 10 Gavrilov, Lubomir 10 Giacomini, Hector J. 10 Jardón-Kojakhmetov, Hildeberto 10 Prohens, Rafel 10 Romanovskiĭ, Valeriĭ Georgievich 9 Boukoucha, Rachid 9 Caubergh, Magdalena 9 Grau, Maite 9 Ichida, Yu 9 Kaper, Tasso J. 9 Martínez, Y. Paulina 9 Messias, Marcelo 9 Peng, Linping 9 Shen, Jianhe 9 Zangeneh, Hamid R. Z. 8 Chung, Kwok-Wai 8 Françoise, Jean-Pierre 8 Freire Macías, Emilio 8 Ibáñez, Santiago 8 Kazemi, Rasool 8 Krupa, Martin 8 Liang, Haihua 8 Vidal, Claudio 8 Wang, Zhaoxia 8 Zhang, Zhifen 8 Županović, Vesna 7 Alvarez, María Jesus 7 Bendjeddou, Ahmed 7 Benterki, Rebiha 7 Chen, Ting 7 Du, Zengji 7 Feng, Zhaosheng 7 Flores, José D. 7 Gonzalez-Yañez, Betsabe 7 Jelbart, Samuel 7 Mañosa, Víctor 7 Mardešić, Pavao 7 Novaes, Douglas Duarte 7 Qin, Bo-Wei 7 Vulpe, Nicolae I. 7 Wang, Jihua 7 Xiong, Yanqin 7 Yu, Jiang 7 Zhang, Tonghua 6 Arancibia-Ibarra, Claudio 6 Broer, Henk W. 6 Chèze, Guillaume 6 Dias, Fabio Scalco 6 Gaiko, Valery A. 6 Gamero, Estanislao 6 Pantazi, Chara ...and 1,222 more Authors all top 5 Cited in 236 Serials 241 Journal of Differential Equations 110 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 76 Qualitative Theory of Dynamical Systems 73 Journal of Mathematical Analysis and Applications 38 Physica D 38 Journal of Dynamics and Differential Equations 38 SIAM Journal on Applied Dynamical Systems 33 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 33 Discrete and Continuous Dynamical Systems. Series B 31 Chaos, Solitons and Fractals 30 Nonlinear Dynamics 26 Nonlinearity 26 Nonlinear Analysis. Real World Applications 25 Bulletin des Sciences Mathématiques 24 Journal of Nonlinear Science 20 Transactions of the American Mathematical Society 19 Applied Mathematics and Computation 18 Discrete and Continuous Dynamical Systems 17 Dynamical Systems 15 Proceedings of the American Mathematical Society 14 Communications in Nonlinear Science and Numerical Simulation 14 Discrete and Continuous Dynamical Systems. Series S 12 Journal of Mathematical Biology 12 Acta Mathematica Sinica. English Series 12 Journal of Dynamical and Control Systems 11 Electronic Journal of Differential Equations (EJDE) 10 Annales de l’Institut Fourier 10 Nonlinear Analysis. Theory, Methods & Applications 9 Journal of Mathematical Physics 9 Mathematical Biosciences 9 Mathematical Methods in the Applied Sciences 9 Advances in Mathematics 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Mathematics and Computers in Simulation 9 Ergodic Theory and Dynamical Systems 9 Applied Mathematics Letters 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Communications on Pure and Applied Analysis 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Rocky Mountain Journal of Mathematics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Mathematical Sciences (New York) 7 Regular and Chaotic Dynamics 7 Journal of Nonlinear Mathematical Physics 7 Journal of Applied Analysis and Computation 6 Journal of Geometry and Physics 6 Journal of Computational and Applied Mathematics 6 Rendiconti del Circolo Matemàtico di Palermo. Serie II 6 Acta Applicandae Mathematicae 6 Journal of Difference Equations and Applications 6 Discrete Dynamics in Nature and Society 6 Mediterranean Journal of Mathematics 5 Applicable Analysis 5 Bulletin of Mathematical Biology 5 Publications Mathématiques 5 Chinese Annals of Mathematics. Series B 5 SIAM Journal on Mathematical Analysis 5 Expositiones Mathematicae 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Boletín de la Sociedad Matemática Mexicana. Third Series 5 Differential Equations and Dynamical Systems 5 Chaos 5 Mathematical Modelling and Analysis 5 Mathematical Biosciences and Engineering 5 Sibirskie Èlektronnye Matematicheskie Izvestiya 4 Inventiones Mathematicae 4 Complexity 4 Differential Equations 4 Nonlinear Analysis. Modelling and Control 4 Bulletin of the Brazilian Mathematical Society. New Series 4 Mathematical Modelling of Natural Phenomena 4 International Journal of Biomathematics 4 The Journal of Mathematical Neuroscience 3 Computers & Mathematics with Applications 3 Journal of Fluid Mechanics 3 Physics Reports 3 Theoretical and Mathematical Physics 3 Duke Mathematical Journal 3 Functional Analysis and its Applications 3 Journal of Computer and System Sciences 3 Results in Mathematics 3 Transactions of the Moscow Mathematical Society 3 Applied Mathematics and Mechanics. (English Edition) 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Acta Mathematicae Applicatae Sinica. English Series 3 Mathematical and Computer Modelling 3 Dynamics and Stability of Systems 3 Science in China. Series A 3 Applied Mathematical Modelling 3 SIAM Review 3 Indagationes Mathematicae. New Series 3 Russian Mathematics 3 Topological Methods in Nonlinear Analysis 3 NoDEA. 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Mathematics & Physics ...and 136 more Serials all top 5 Cited in 50 Fields 1,263 Ordinary differential equations (34-XX) 578 Dynamical systems and ergodic theory (37-XX) 261 Biology and other natural sciences (92-XX) 96 Partial differential equations (35-XX) 61 Mechanics of particles and systems (70-XX) 49 Global analysis, analysis on manifolds (58-XX) 27 Numerical analysis (65-XX) 24 Several complex variables and analytic spaces (32-XX) 23 Differential geometry (53-XX) 22 Fluid mechanics (76-XX) 19 Algebraic geometry (14-XX) 17 Manifolds and cell complexes (57-XX) 13 Difference and functional equations (39-XX) 13 Probability theory and stochastic processes (60-XX) 13 Computer science (68-XX) 12 Relativity and gravitational theory (83-XX) 10 Systems theory; control (93-XX) 9 Mechanics of deformable solids (74-XX) 8 Measure and integration (28-XX) 8 Information and communication theory, circuits (94-XX) 7 Nonassociative rings and algebras (17-XX) 7 Operator theory (47-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Quantum theory (81-XX) 6 Geophysics (86-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Commutative algebra (13-XX) 4 Functions of a complex variable (30-XX) 4 General topology (54-XX) 4 Optics, electromagnetic theory (78-XX) 4 Astronomy and astrophysics (85-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 2 Mathematical logic and foundations (03-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Potential theory (31-XX) 1 Geometry (51-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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