What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (65.35%)
- Vector field (33.66%)
- Pure mathematics (26.73%)
What were the highlights of his more recent work (between 2010-2015)?
- Mathematical analysis (65.35%)
- Limit (19.80%)
- Singular perturbation (20.79%)
In recent papers he was focusing on the following fields of study:
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.
Between 2010 and 2015, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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