The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Fedorov, Yuri (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)

Date:	2014
Abstract:	We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of some parameters of the curves. The systems can be regarded as extensions of the well-studied Picard-Fuchs equations for periods of complete integrals of first and second kind on odd hyperelliptic curves. The periods we consider are linear combinations of the action variables of several integrable systems, in particular the generalized Neumann system with polynomial separable potentials. Thus the solutions of the extended Picard-Fuchs equations can be used to study various properties of the actions.
Grants:	Ministerio de Ciencia e Innovación MTM2009-06973 Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Journal of Mathematical Physics, Vol. 55 (2014) , p. 32703, ISSN 1089-7658

DOI: 10.1063/1.4868965

Postprint 8 p, 280.6 KB

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