Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas

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dc.contributor.authorOliveira, Regilene
dc.contributor.authorRezende, Alex C.
dc.contributor.authorSchlomiuk, Dana
dc.contributor.authorVulpe, Nicolae
dc.date.accessioned2022-09-26T18:48:14Z
dc.date.available2022-09-26T18:48:14Z
dc.date.issued2017-11-28
dc.description.abstractLet QSH be the whole class of non-degenerate planar quadratic differential systems possessing at least one invariant hyperbola. We classify this family of systems, modulo the action of the group of real affine transformations and time rescaling, according to their geometric properties encoded in the configurations of invariant hyperbolas and invariant straight lines which these systems possess. The classification is given both in terms of algebraic geometric invariants and also in terms of affine invariant polynomials. It yields a total of 205 distinct such configurations. We have 162 configurations for the subclass QSH(η>0) of systems which possess three distinct real singularities at infinity in P2(ℂ), and 43 configurations for the subclass QSH(η=0) of systems which possess either exactly two distinct real singularities at infinity or the line at infinity filled up with singularities. The algebraic classification, based on the invariant polynomials, is also an algorithm which makes it possible to verify for any given real quadratic differential system if it has invariant hyperbolas or not and to specify its configuration of invariant hyperbolas and straight lines.
dc.description.departmentMathematics
dc.formatText
dc.format.extent122 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationOliveira, R. D. S., Rezende, A. C., Schlomiuk, D., & Vulpe, N. (2017). Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas. <i>Electronic Journal of Differential Equations, 2017</i>(295), pp. 1-122.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16167
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectQuadratic differential systems
dc.subjectAlgebraic solution
dc.subjectConfiguration of algebraic solutions
dc.subjectAffine invariant polynomials
dc.subjectGroup action
dc.titleGeometric and algebraic classification of quadratic differential systems with invariant hyperbolas
dc.typeArticle

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