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- Freddy Dumortier

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
32
Citations
4,033
110
World Ranking
2435
National Ranking
31

- Mathematical analysis
- Geometry
- Algebra

His scientific interests lie mostly in Mathematical analysis, Vector field, Pure mathematics, Limit cycle and Elliptic integral. His Mathematical analysis study combines topics in areas such as Nilpotent and Bifurcation diagram. As part of the same scientific family, Freddy Dumortier usually focuses on Vector field, concentrating on Singularity and intersecting with Cusp, Solenoidal vector field and Submanifold.

His work on Codimension as part of general Pure mathematics research is often related to Quadratic programming, thus linking different fields of science. His Limit cycle research is multidisciplinary, incorporating perspectives in Scalar field, Polynomial and Scalar. His work in Elliptic integral tackles topics such as Infimum and supremum which are related to areas like Hamiltonian vector field and Mathematical physics.

- Canard Cycles and Center Manifolds (353 citations)
- Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3 (147 citations)
- Hilbert′s 16th Problem for Quadratic Vector Fields (91 citations)

His primary areas of study are Mathematical analysis, Vector field, Pure mathematics, Gravitational singularity and Singular perturbation. In his study, which falls under the umbrella issue of Mathematical analysis, Geometry is strongly linked to Bifurcation. His Vector field research includes elements of Phase portrait, Singularity, Invariant and Elliptic integral.

In his work, Abelian integral is strongly intertwined with Planar vector fields, which is a subfield of Pure mathematics. His study in Gravitational singularity is interdisciplinary in nature, drawing from both Ordinary differential equation and Singular solution. Freddy Dumortier focuses mostly in the field of Singular perturbation, narrowing it down to matters related to Singular point of a curve and, in some cases, Transformation.

- Mathematical analysis (65.35%)
- Vector field (33.66%)
- Pure mathematics (26.73%)

- Mathematical analysis (65.35%)
- Limit (19.80%)
- Singular perturbation (20.79%)

Freddy Dumortier spends much of his time researching Mathematical analysis, Limit, Singular perturbation, Limit cycle and Jump. His work on Periodic orbits as part of general Mathematical analysis research is frequently linked to Context, thereby connecting diverse disciplines of science. His work carried out in the field of Limit brings together such families of science as Bogdanov–Takens bifurcation, Pure mathematics, Parameter space, Vector field and Polynomial.

His biological study spans a wide range of topics, including Center manifold and Topology. His work deals with themes such as Invariant manifold, Divergence and Nilpotent, which intersect with Singular perturbation. In his study, Degree and Type is strongly linked to Discrete mathematics, which falls under the umbrella field of Limit cycle.

- Classical Liénard equations of degree n⩾6 can have [n−12]+2 limit cycles (42 citations)
- About the unfolding of a Hopf-zero singularity (34 citations)
- Cyclicity of common slow–fast cycles (31 citations)

- Mathematical analysis
- Geometry
- Algebra

Limit, Limit cycle, Mathematical analysis, Singular perturbation and Vector field are his primary areas of study. His studies deal with areas such as Discrete mathematics, Conjecture, Counterexample and Degree as well as Limit cycle. Freddy Dumortier combines subjects such as Bogdanov–Takens bifurcation, Phase portrait, Parameter space, Phase plane and Line with his study of Mathematical analysis.

Many of his studies involve connections with topics such as Bifurcation diagram and Singular perturbation. The study incorporates disciplines such as Sequence and Divergence in addition to Vector field.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Canard Cycles and Center Manifolds

Freddy Dumortier;Robert H. Roussarie.

**(1996)**

580 Citations

Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3

F. Dumortier;R. Roussarie;J. Sotomayor.

Ergodic Theory and Dynamical Systems **(1987)**

216 Citations

Techniques in the Theory of Local Bifurcations: Blow-Up, Normal Forms, Nilpotent Bifurcations, Singular Perturbations

Freddy Dumortier.

**(1993)**

179 Citations

Hilbert′s 16th Problem for Quadratic Vector Fields

Freddy Dumortier;R Roussarie;C Rousseau.

Journal of Differential Equations **(1994)**

143 Citations

Bifurcations of planar vector fields : nilpotent singularities and Abelian integrals

Freddy Dumortier;Robert H. Roussarie;Jorge Sotomayor;Henryk Żoładek.

**(1991)**

139 Citations

Perturbations from an Elliptic Hamiltonian of Degree Four: I. Saddle Loop and Two Saddle Cycle☆

Freddy Dumortier;Chengzhi Li.

Journal of Differential Equations **(2001)**

136 Citations

Cubic Lienard equations with linear damping

F Dumortier;C Rousseau.

Nonlinearity **(1990)**

132 Citations

More limit cycles than expected in Liénard equations

Freddy Dumortier;Daniel Panazzolo;Robert H. Roussarie.

Proceedings of the American Mathematical Society **(2007)**

130 Citations

Perturbations from an Elliptic Hamiltonian of Degree Four

Freddy Dumortier;Chengzhi Li.

Journal of Differential Equations **(2001)**

129 Citations

Perturbation from an elliptic Hamiltonian of degree four—IV figure eight-loop

Freddy Dumortier;Chengzhi Li.

Journal of Differential Equations **(2003)**

127 Citations

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