Results overview: Found 7 records in 0.02 seconds.
Articles, 5 records found
Research literature, 2 records found
Articles 5 records found  
1.
14 p, 337.6 KB Local Darboux first integrals of analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
In this paper we discuss local and formal Darboux first integrals of analytic differential systems, using the theory of Poincaré Dulac normal forms. We study the effect of local Darboux integrability on analytic normalization. [...]
2014 - 10.1016/j.bulsci.2013.09.007
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 71-88  
2.
11 p, 532.6 KB Morphisms and inverse problems for Darboux integrating factors / 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)
Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. [...]
2013 - 10.1017/S0308210511001430
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, Vol. 143 Núm. 6 (2013) , p. 1291-1302  
3.
15 p, 373.2 KB First integrals of local analytic differential systems / 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)
We investigate formal and analytic first integrals of local analytic ordinary differential equations near a stationary point. A natural approach is via the Poincaré-Dulac normal forms: If there exists a formal first integral for a system in normal form then it is also a first integral for the semisimple part of the linearization, which may be seen as "conserved" by the normal form. [...]
2012 - 10.1016/j.bulsci.2011.10.003
Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 342-359  
4.
22 p, 450.4 KB Inverse problems in Darboux' theory of integrability / Christopher, Colin J. (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  
5.
23 p, 715.3 KB Darboux integrating factors: Inverse problems / Christopher, Colin J. (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 Matematica Aplicada I) ; Walcher, Sebastian (Lehrstuhl A fur Mathematik (Germany))
2011 - 10.1016/j.jde.2010.10.013
Journal of Differential Equations, Vol. 250 Núm. 1 (2011) , p. 1-25  

Research literature 2 records found  
1.
33 p, 282.8 KB Inverse Problems for multiple invariant curves / Cristopher, 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 Matematica Aplicada I) ; Walcher, Sebastian (RWTH Aachen) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. [...]
Centre de Recerca Matemàtica 2006 (Prepublicacions del Centre de Recerca Matemàtica ; 671)  
2.
17 p, 213.1 KB Inverse problems for invariant algebraic curves : explicit computations / Cristopher, 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 Matematica Aplicada I) ; Walcher, Sebastian (RWTH Aachen) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. [...]
Centre de Recerca Matemàtica 2007 (Prepublicacions del Centre de Recerca Matemàtica ; 774)  

Interested in being notified about new results for this query?
Set up a personal email alert or subscribe to the RSS feed.