Inverse problems in Darboux' theory of integrability

Chara Pantazi; Colin Christopher; Jaume Llibre; Sebastian Walcher

doi:10.1007/s10440-012-9671-9

Inverse problems in Darboux' theory of integrability

Chara Pantazi, Colin Christopher, Jaume Llibre, Sebastian Walcher

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Resum

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. We also prove a new result, viz. a general finiteness theorem for the case of prescribed integrating factors. A number of relevant examples and applications is included.

Idioma original	Anglès
Pàgines (de-a)	0101-126
Nombre de pàgines	26
Revista	Acta Applicandae Mathematicae
Volum	120
DOIs	https://doi.org/10.1007/s10440-012-9671-9
Estat de la publicació	Publicada - 2012

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10.1007/s10440-012-9671-9

https://ddd.uab.cat/record/150516

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Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones
Torregrosa i Arús, J. (Investigador/a principal), Cima Mollet, A. M. (Investigador/a), Gasull Embid, A. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Mañosa Fernández, V. (Investigador/a), Artes Ferragud, J. C. (Investigador/a), Llibre Salo, J. (Investigador/a), Corbera Subirana, M. (Investigador/a), Pantazi ., C. (Investigador/a), Garrido Pelaez, J. M. (Col.laborador/a), Mañosas Capellades, F. (Col.laborador/a), Jimenez Ruiz, J. J. (Col.laborador/a), Mayayo Cortasa, T. (Col.laborador/a) & Villadelprat Yague, J. (Investigador/a)
Fons Social Europeu
1/09/23 → 31/08/26
Projecte: Projectes i Ajuts a la Recerca

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title = "Inverse problems in Darboux' theory of integrability",

abstract = "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. We also prove a new result, viz. a general finiteness theorem for the case of prescribed integrating factors. A number of relevant examples and applications is included.",

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AU - Christopher, Colin

AU - Llibre, Jaume

AU - Walcher, Sebastian

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AB - 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. We also prove a new result, viz. a general finiteness theorem for the case of prescribed integrating factors. A number of relevant examples and applications is included.

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JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

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Inverse problems in Darboux' theory of integrability

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Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones

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