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Freddy Dumortier

Freddy Dumortier

D-Index & Metrics

Mathematics

D-Index
38
Citations
5323
World Ranking
2376
National Ranking
32

Overview

Freddy Dumortier is affiliated with Hasselt University in Belgium and has contributed extensively to the fields of Mathematics, Physics and Astronomy, and Computer Science. Their research spans multiple disciplines, including advanced differential equations, dynamical systems, quantum chaos, nonlinear dynamics, and mathematical physics.

The scientist has produced a considerable body of work with 17 publications in Mathematics, 15 in Physics and Astronomy, and 7 in Computer Science. Within these fields, their research further focuses on subfields such as:

  • Statistical and Nonlinear Physics
  • Geometry and Topology
  • Computer Networks and Communications
  • Mathematical Physics
  • Numerical Analysis

The main topics of interest cover:

  • Advanced Differential Equations and Dynamical Systems
  • Quantum chaos and dynamical systems
  • Nonlinear Dynamics and Pattern Formation
  • Stochastic dynamics and bifurcation
  • Advanced mathematical theories
  • Differential Equations and Numerical Methods
  • Advanced Thermodynamics and Statistical Mechanics

Freddy Dumortier has collaborated frequently with researchers Peter De Maesschalck and Robert Roussarie, each with a notable number of joint publications. Their works have been published predominantly in:

  • Journal of Differential Equations
  • Regular and Chaotic Dynamics
  • Nonlinearity

Some notable recent papers authored or coauthored by Dumortier include:

  • "A flow box theorem for 2d slow-fast vector fields and diffeomorphisms and the slow log-determinant integral" (2022), Journal of Differential Equations
  • "Side-Comparison for Transition Maps in Multi-Layer Canard Problems" (2023), Regular and Chaotic Dynamics
  • "Corrigendum to "A flow box theorem for 2d slow-fast vector fields and diffeomorphisms and the slow log-determinant integral"" (2024), Journal of Differential Equations
  • "A systematic study of two-dimensional 2-layer canard cycles" (2025), Nonlinearity

Dumortier has also authored a book titled Canard Cycles, published in 2021 by Springer International Publishing, which has been cited multiple times.

Best Publications

  • Canard Cycles and Center Manifolds

    Freddy Dumortier;Robert H. Roussarie

  • Singularities of vector fields on the plane

    Unknown

  • 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

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

    Freddy Dumortier

  • Bifurcations of planar vector fields : nilpotent singularities and Abelian integrals

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

  • Cubic Lienard equations with linear damping

    F Dumortier;C Rousseau

  • Hilbert′s 16th Problem for Quadratic Vector Fields

    Freddy Dumortier;R Roussarie;C Rousseau

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

    Freddy Dumortier;Chengzhi Li

  • More limit cycles than expected in Liénard equations

    Freddy Dumortier;Daniel Panazzolo;Robert H. Roussarie

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

    Freddy Dumortier;Chengzhi Li

  • Perturbations from an Elliptic Hamiltonian of Degree Four

    Freddy Dumortier;Chengzhi Li

  • Time analysis and entry-exit relation near planar turning points

    P. De Maesschalck;F. Dumortier

  • Abelian integrals and limit cycles

    Freddy Dumortier;Robert Roussarie

  • On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations

    Freddy Dumortier;Chengzhi Li

  • Perturbation from an elliptic Hamiltonian of degree four—III global centre

    Freddy Dumortier;Chengzhi Li

  • Unfolding of a Quadratic Integrable System with Two Centers and Two Unbounded Heteroclinic Loops

    Freddy Dumortier;Chengzhi Li;Zifen Zhang

  • Multiple Canard Cycles in Generalized Liénard Equations

    Freddy Dumortier;Robert Roussarie

  • Classical Liénard equations of degree n⩾6 can have [n-1/2]+2 limit cycles

    P. De Maesschalck;F. Dumortier

  • Canard solutions at non-generic turning points

    Peter De Maesschalck;Freddy Dumortier

  • QUADRATIC LIENARD EQUATIONS WITH QUADRATIC DAMPING

    Unknown

  • GENERIC 3-PARAMETER FAMILIES OF PLANAR VECTOR-FIELDS, UNFOLDINGS OF SADDLE, FOCUS AND ELLIPTIC-SINGULARITIES WITH NILPOTENT LINEAR PARTS

    Freddy Dumortier;R Roussarie;J Sotomayor

  • Singularities of vector fields on

    F Dumortier;S Ibáñez

Frequent Co-Authors

Tasso J. Kaper
Tasso J. Kaper Boston University
Hendrik Broer
Hendrik Broer University of Groningen
Carles Simó
Carles Simó University of Barcelona
Floris Takens
Floris Takens University of Groningen
Martin Wechselberger
Martin Wechselberger University of Sydney

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