Schlomiuk, Dana
 Adjunct Professor

Faculty of Arts and Science  Department of Mathematics and Statistics
AndréAisenstadt
Courriels
Affiliations
 Membre Centre de recherches mathématiques
Research area
 Bifurcation theory
 Center singularity
 Limit cycle
 Global analysis of quadratic vector fields
 Group action
 Invariant algebraic curves
 Polynomial vector fields
 Polynomial invariants
 Dynamical systems
 Darboux and Liouville integrability
 Analysis and probability
Student supervision Expand all Collapse all
Abstract
Research projects Expand all Collapse all
Global geometry of families of polynomial vector fields CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2020  2027
GLOBAL GEOMETRY OF PLANAR VECTOR FIELDS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2015  2022
GEOMETRY AND ANALYSES OF PLANAR ANALYTIC VERTOC FIELDS / 2010  2014
GEOMETRY AND ANALYSES OF PLANAR ANALYTIC VERTOC FIELDS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 1994  2016
Selected publications Expand all Collapse all
On the limit cycles bifurcating from an ellipse of a quadratic center
Global configurations of singularities for quadratic differential systems with total finite multiplicity three and at most two real singularities
Geometric configurations of singularities for quadratic differential systems with total finite multiplicity $m_f=2$
Topological and polynomial invariants, moduli spaces, in classification problems of polynomial vector fields
Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities
Mathematical destinies
Geometric configurations of singularities for quadratic differential systems with total finite multiplicity lower than 2
New developments based on the mathematical legacy of C. S. Sibirschi
Geometry of quadratic differential systems with a weak focus of second order
Global topological classification of LotkaVolterra quadratic differential systems
The geometry of quadratic polynomial differential systems with a weak focus and an invariant straight line
Bifurcation diagrams and moduli spaces of planar quadratic vector fields with invariant lines of total multiplicity four and having exactly three real singularities at infinity
Preface [Classical problems on planar polynomial vector fields]
Global classification of the planar LotkaVolterra differential systems according to their configurations of invariant straight lines
Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity
The full study of planar quadratic differential systems possessing a line of singularities at infinity
On general algebraic mechanisms for producing centers in polynomial differential systems
Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four
Planar quadratic differential systems with invariant straight lines of total multiplicity four
The geometry of quadratic differential systems with a weak focus of second order
On finiteness in differential equations and Diophantine geometry
Finiteness problems in differential equations and diophantine geometry
Geometry of quadratic differential systems in the neighborhood of infinity
Planar quadratic vector fields with invariant lines of total multiplicity at least five
Aspects of planar polynomial vector fields: Global versus local, real versus complex, analytic versus algebraic and geometric
The Geometry of Quadratic Differential systems with a weak focus of third order
On the geometric structure of the class of planar quadratic differential systems
The mathematical legacy of C. S. Sibirsky, basis for future work
The geometry in the neighborhood of infinity of quadratic differential systems with a weak focus
On the geometry in the neighborhood of infinity of quadratic differential systems with a weak focus
On the geometry of planar vector fields
Basic AlgebroGeometric concepts in the study of planar polynomial vector fields
On the global analysis of the planar quadratic vector fields
Summing up the dynamics of quadratic Hamiltonian systems with a center
The centers in the reduced Kukles system
Cubic vector fields symmetric with respect to a center
Elementary first integrals and algebraic invariant curves of differential equations
Elementary first integrals of differential equations and invariant algebraic curves
Algebraic and geometric aspects of the theory of planar polynomial vector fields
Algebraic particular integrals, integrability and the problem of the center
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
Une caract?risation g?om?trique g?n?rique des champs de vecteurs quadratiques avec un centre
Integrability of plane quadratic vector fields
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems
Generalized Hopf bifurcations and applications to planar quadratic systems
La logica dei topos
Dimensions of orbits and strata in complex and real classical Lie algebras
Versal deformations of elements of real classical Lie algebras
Logique des topos (introduction ? la th?orie des topos ?l?mentaires)
Logique des topos
Topos di Grothendieck e topos di Lawvere e Tierney
An elementary theory of the category of topological spaces