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Author ID: dumortier.freddy Recent zbMATH articles by "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

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

Publications by Year

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 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
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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. Nonlinear Differential Equations and Applications
3 Mathematical Physics, Analysis and Geometry
3 Communications in Contemporary Mathematics
3 Applied Mathematics E-Notes
3 Advances in Difference Equations
3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 Journal of Siberian Federal University. Mathematics & Physics
...and 136 more Serials
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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)

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