Author： Douai Antoine
Publisher： Springer Publishing Company
ISSN： 1079-2724
Source： Journal of Dynamical and Control Systems, Vol.11, Iss.4, 2005-10, pp. : 495-526
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
We study Abelian integrals associated with a tame polynomial function and their Picard–Fuchs equations using the theory of algebraic Gauss–Manin systems. Especially, we look for a basis of the Petrov module, in which the Picard–Fuchs equations become as simple as possible. As an application, we discuss the related Riemann–Hilbert problem and prove that it has a positive answer under some conditions. In this case, we compute the Jordan normal form of the residue matrices of the corresponding Fuchsian system in terms of local data.
Related content
On the Riemann–Hilbert Problem in Dimension 4
Journal of Dynamical and Control Systems, Vol. 6, Iss. 2, 2000-04 ,pp. :
Access to resources
Recommend
A Riemann–Hilbert approach for the Degasperis–Procesi equation
Nonlinearity, Vol. 26, Iss. 7, 2013-07 ,pp. :