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Resultats globals: 6 registres trobats en 0.02 segons.
Articles, 6 registres trobats
Articles 6 registres trobats  
1.
24 p, 376.6 KB Three-dimensional Lotka-Volterra systems with 3:−1:2-Resonance / Aziz, Waleed (Tishk International University. Information Technology Department (Iraq)) ; Christopher, Colin (Plymouth University. School of Engineering, Computing and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka-Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. [...]
2021 - 10.1007/s00009-021-01809-2
Mediterranean Journal of Mathematics, Vol. 18, Issue 4 (August 2021) , art. 167  
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2.
16 p, 769.0 KB On planar polynomial vector fields with elementary first integrals / Christopher, Colin (School of Computing, Electronics and Mathematics (UK)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Walcher, Sebastian (Lehrstuhl A für Mathematik. RWTH Aachen (Germany))
We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. [...]
2019 - 10.1016/j.jde.2019.05.007
Journal of differential equations, Vol. 267, Issue 8 (October 2019) , p. 4572-4588  
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3.
22 p, 450.4 KB Inverse problems in Darboux' theory of integrability / Christopher, Colin (University of Plymouth(UK). Department of Mathematics and Statistics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik)
The Darboux theory of integrability for planar polynomial differential equations is a classical field, with connections to Lie symmetries, differential algebra and other areas of mathematics. In the present paper we introduce the concepts, problems and inverse problems, and we outline some recent results on inverse problems. [...]
2012 - 10.1007/s10440-012-9671-9
Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications, Vol. 120 (2012) , p. 101-126  
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4.
23 p, 715.3 KB Darboux integrating factors: Inverse problems / Christopher, Colin (University of Plymouth. Department of Mathematics and Statistics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Walcher, Sebastian (Lehrstuhl A fur Mathematik (Germany))
We discuss planar polynomial vector fields with prescribed Darboux integrating factors, in a nondegenerate affine geometric setting. We establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems, and show that the space of vector fields with a given integrating factor, modulo a subspace of explicitly known "standard" vector fields, has finite dimension. [...]
2011 - 10.1016/j.jde.2010.10.013
Journal of differential equations, Vol. 250 Núm. 1 (2011) , p. 1-25  
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5.
12 p, 367.5 KB On the integrability of some three-dimensional Lotka-Volterra equations with rank-1 resonances / Aziz, Waleed (University of Salahaddin. Department of Mathematics) ; Christopher, Colin (Plymouth University. School of Computing and Mathematics)
We investigate the local integrability in C3 of some three-dimensional Lotka-Volterra equations at the origin with (p : q : r)-resonance, x˙ = P = x(p + ax + by + cz), y˙ = Q = y(q + dx + ey + fz), z˙ = R = z(r + gx + hy + kz). [...]
2014 - 10.5565/PUBLMAT_Extra14_02
Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 37-48  
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6.
29 p, 233.7 KB Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in C2 / Christopher, C. ; Rousseau, C.
In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. [...]
2001 - 10.5565/PUBLMAT_45101_04
Publicacions matemàtiques, V. 45 N. 1 (2001) , p. 95-123  
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6 Christopher, Colin
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