Results 1 to 10 of about 99,903 (246)
Invariant Algebraic Curves of Generalized Liénard Polynomial Differential Systems [PDF]
Mathematics, 2022 In this study, we focus on invariant algebraic curves of generalized Liénard polynomial differential systems x′=y, y′=−fm(x)y−gn(x), where the degrees of the polynomials f and g are m and n, respectively, and we correct some results previously stated.
Jaume Giné, Jaume Llibre
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On the algebraic invariant curves of plane polynomial differential systems [PDF]
Journal of Physics A: Mathematical and General, 2000 We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the
Alexei Tsygvintsev +12 more
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On a class of invariant algebraic curves for Kukles systems
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper we give a new upper bound for the degree of a class of transversal to infinity invariant algebraic curves for polynomial Kukles systems of arbitrary degree.
Osvaldo Osuna +2 more
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Inverse problems for invariant algebraic curves : explicit computations [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2007 Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant.
Cristopher, Colin +4 more
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A linking invariant for algebraic curves [PDF]
L’Enseignement Mathématique, 2020 We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generalization of the \mathcal I -invariant of line arrangements developed by ...
Guerville-Ballé, Benoît +1 more
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On Control Polygons of Planar Sextic Pythagorean Hodograph Curves
Mathematics, 2023 In this paper, we analyze planar parametric sextic curves to determine conditions for Pythagorean hodograph (PH) curves. By expressing the curves to be analyzed in the complex form, the analysis is conducted in algebraic form.
Yujun Li +3 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research.
Regilene Oliveira +3 more
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Explicit travelling waves and invariant algebraic curves
Nonlinearity, 2015 In this paper we introduce a precise definition of algebraic traveling wave solution for general n-th order partial differential equations. All examples of explicit traveling waves known by the authors fall in this category. Our main result proves that algebraic traveling waves exist if and only if an associated n- dimensional first order ordinary ...
Gasull, Armengol, Giacomini, Hector
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Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models
Cubo, 2021 We prove that for certain polynomial differential equations in the plane arising from predator-prey type III models with generalized rational functional response, any algebraic solution should be a rational function. As a consequence, limit cycles, which
Homero G. Díaz-Marín, Osvaldo Osuna
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Acta et Commentationes: Ştiinţe Exacte şi ale Naturii, 2023 In this paper for a cubic differential system with a singular point
Dumitru Cozma
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