Rousseau, Christiane
 Adjunct and Emeritus and Honorary professor

Faculty of Arts and Science  Department of Mathematics and Statistics
AndréAisenstadt Office 5231
Courriels
Affiliations
 Membre Centre de recherches mathématiques
 Membre CRM Centre de recherches mathématiques
Research area
 Singularity
 Linear differential systems
 Dynamical systems
 Unfoldings of singularities
 Limit cycle
 Predatorprey system
 Normal forms
 Hilbert's sixth problem
 Parabolic point
 Analysis and probability
My research interests are around dynamical systems in small dimension, either ODE or difference equations.
In the case of ODE, I am interested in the qualitative theory of ODE and the development of methods allowing understanding the geometric organization of the solutions, often summarized in the phase portrait. I am especially interested to parameter dependent ODE and bifurcation analysis: bifurcations correspond to qualitative changes on the phase portraits occurring for particular values of the parameters. I am interested in applications to Hilbert 19s 16th problem on one side and, occasionally, to some predatorprey models in mathematical biology.
The main part of my recent research deals with the study of equilibrium positions of analytic dynamical systems depending on parameters, more precisely with the problem
of analytic classification of singularities of families of dynamical systems depending on parameters: when are two analytic families of dynamical systems equivalent modulo an analytic change of parameters and possibly a reparameterization of time? There are many obstructions to such equivalences and I am interesting in understanding their geometric meaning.
I am also very involved in popularization of mathematics and the training of future high school teachers.
I was the instigator and international coordinator of the international year Mathematics of Planet Earth 2013 (MPE2013).
Student supervision Expand all Collapse all
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Abstract
Research projects Expand all Collapse all
Centre de recherches mathématiques (CRM) FRQNT/Fonds de recherche du Québec  Nature et technologies (FQRNT) / 2022  2029
Singularities of dynamical systems and their unfoldings CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016  2024
Singularities of dynamical systems and their unfoldings CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016  2023
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec  Nature et technologies (FQRNT) / 2015  2023
PROJETS SPECIAUX 13PS178863 (HORS RECHERCHE) PARTICIPATION FINANCIERE DU FRQNT A L'IMPRESSION ET A LA DISTRIBUTION DE LA REVUE ACCROMATH EN AFRIQUE FRQNT/Fonds de recherche du Québec  Nature et technologies (FQRNT) / 2013  2014
NORMAL FORMS AND BIFURCATIONS OF VECTOR FIELDS / 2010  2014
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec  Nature et technologies (FQRNT) / 2008  2016
UPGRADE OF CRM RESEARCH COMPUTER NETWORK / 2008  2008
NORMAL FORMS AND BIFURCATIONS OF VECTOR FIELDS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 1994  2017
Selected publications Expand all Collapse all
Traduction brésilienne : matemática e Atualidade
Construire une image médicale
Traduction brésilienne : matemática e Atualidade
Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank $k$
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point
Cristaux
Passera, passera pas?
Moduli space of unfolded differential linear systems with an irregular singularity of Poincaré rank 1
How Inge Lehmann discovered the inner core of the Earth
Mathématiques de la planète Terre 2013 et chimie
Comment Inge Lehmann a découvert le noyau interne de la Terre
L'équation du temps
Des coquillages aux pelages
Que signifie dimension?
Voyager aux confins du système solaire en économisant l'énergie
The modulus of cusps in conformal geometry
The equation of time
Traduction allemande : Mathematik und technologie
The modulus of unfoldings of cusps in conformal geometry
Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1
L'effet papillon
Les sphères de Dandelin
Teorema do ponto fixo de Banach e aplicações
Au delà de l'effet papillon
The center and cyclicity problems
Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III
The modulus of analytic classification for the unfolding of the codimensionone flip and Hopf bifurcations
Apprendre à frauder ou à détecter les fraudes
Bifurcation analysis of a generalized Gause model with prey harvesting anf a geenralized Holling Response of type III
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a codimension 1 resonant diffeomorphism or resonant saddle
Study of the cyclicity of some degenerate graphics inside quadratic systems
Traduction anglaise : Mathematics and technology
Mathématiques et technologie
Finite cyclicity of nilpotent graphics of pptype surrounding a center
Analytical moduli for unfoldings of saddlenode vector fields
Bifurcation analysis of a predatorprey system with generalised Holling type III functional response
The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation
Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle
The root extraction problem
The moduli space of germs of generic families and analytic diffeomorphisms unfolding a parabolic fixed point
Modulus of orbital analytic classification for a family unfolding a saddlenode
Normalizable, integrable and linearizable saddle points in the LotkaVolterra system
Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms
Normalizability, synchronicity, and relative exactness for vector fields in $\Bbb C^2$
PPgraphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem
Normal forms, bifurcations and finiteness problems in differential equations
Normalizable, integrable, and linearizable saddle points for complex quadratic systems in $\Bbb C^2$
Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems
Normal forms near a saddlenode and applications to finite cyclicity of graphics
Normal forms, bifurcations and finiteness problems in differential equations?
Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $\Bbb C^2$
Finite cyclicity of finite codimension nondegenerate homoclinic loops with real eigenvalues in $\Bbb R^3$
Genericity conditions for finite cyclicity of elementary graphics
Global study of a family of cubic Liénard equations
Cyclicity of graphics with semihyperbolic points inside quadratic systems
Codimensionthree unfoldings of reflectionally symmetric planar vector fields
Local bifurcations of critical periods in the reduced Kukles system
Darboux linearization and isochronous centers with a rational first integral
Almost planar homoclinic loops in ${\bf R}^3$
A stratum of cubic vector fields with an integrable saddle and $Z_2\times Z_2$ symmetry
Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
Cubic vector fields symmetric with respect to a center
Linearization of isochronous centers
The centres in the reduced Kukles system
Hilbert's 16th problem for quadratic vector fields
Elementary graphics of cyclicity $1$ and $2$
Local bifurcation of critical periods in vector fields with homogeneous nonlinearities of the third degree
Bifurcation at infinity in polynomial vector fields
Bifurcations et orbites périodiques de champs de vecteurs
Zeroes of complete elliptic integrals for $1:2$ resonance
Codimension $2$ symmetric homoclinic bifurcations and application to $1:2$ resonance
Cubic Liénard equations with linear damping
Codimension $1$ and $2$ bifurcations of fixed points of diffeomorphisms and periodic solutions of vector fields
A simple proof for the unicity of the limit cycle in the BogdanovTakens system
A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: the cusp of order $4$
Saddle quantities and applications
Elementary characterization of orbits and strata in the classical Lie and Jordan algebras
Generalized Hopf bifurcations and applications to planar quadratic systems
Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation
ClebschGordan coefficients for ${\rm SU}(5)$ unification models
Spectral decomposition theorem for real symmetric matrices in topoi and applications
ClebschGordan coefficients for $E_{6}$ and ${\rm SO}(10)$ unification models
Versal deformations of elements of classical Jordan algebras
ClebschGordan coefficients for ${\rm SU}(5)\supset{\rm SU}(3)\times{\rm SU}(2)\times{\rm U}(1)$ theories
Versal deformations of elements of real classical Lie algebras
Complex orthogonal and symplectic matrices depending on parameters
Dimensions of orbits and strata in complex and real classical Lie algebras
Formes normales des matrices rectangulaires dans un topos et applications
Nombres réels et complexes dans les topos spatiaux
Topos theory and complex analysis