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The codimension of the phase portraits for degenerate quadratic differential systems
Authors: Joan Carles Artés, Nicolae Vulpe
Keywords: quadratic vector field, infinite and finite singularities, codimension, affine invariant polynomial, Poincare compactification, configuration of singularities, topological equivalence relation
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Keywords: quadratic vector field, infinite and finite singularities, codimension, affine invariant polynomial, Poincare compactification, configuration of singularities, topological equivalence relation
Abstract
In this paper we present a complete study of degenerate quadratic differential systems, i.e. the polynomials from right-hand sides of these systems are not co-prime. We give the complete set of their phase portraits together with the necessary and sufficient conditions for the realization of each one of them. These conditions are given in using invariant polynomials and we present here the ``bifurcation" diagram directly in the space $\mathbb{R}^{12}$ of the whole set of the parameters of the quadratic systems. This paper is part of a project whose ultimate goal is the complete classification of all topologically distinct phase portraits of quadratic systems modulo limit cycles. We also provide a label for each phase portrait inside the global codification related to the global configurations of singularities and their topological codimensions.J.C. Artés
Departament de Matem`atiques, Universitat Aut`onoma de
Barcelona, 08193 Bellaterra, Barcelona, Spain
E-mail:
Nicolae Vulpe
Institute of Mathematics and Computer Science,
Moldova State University
E-mail:
Departament de Matem`atiques, Universitat Aut`onoma de
Barcelona, 08193 Bellaterra, Barcelona, Spain
E-mail:
Nicolae Vulpe
Institute of Mathematics and Computer Science,
Moldova State University
E-mail:
DOI
https://doi.org/10.56415/basm.y2024.i3.p29Fulltext
– 1.13 Mb
Contents
- Existence of positive periodic solution of second-order neutral differential equations with distributed deviating arguments
- Some Characterizations of Generalized Middle Bol Loops
- The codimension of the phase portraits for degenerate quadratic differential systems
- Evolution Time of Stochastic Systems with Multiple Final Sequences of States
- Integrated MILP model for job and crew scheduling to minimize job earliness and tardiness while balancing employee workload
- Remotely Almost Periodic Motions of Dynamical Systems
- On LCA groups with local ring of continuous endomorphisms
- Characteristic Properties of Centrally Symmetric Convex Sets
- The application of 14D Ricci-flat metrics to the equations of rotation of a top
