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Moments on Riemann surfaces and hyperelliptic Abelian integrals
Moments Riemann surfaces hyperelliptic Abelian integrals Dynamical Systems
2011/9/9
Abstract: In the present paper we solve the following different but interrelated problems: (a) the moment problem on Riemann surfaces, (b) the vanishing problem of polynomial Abelian integrals of dime...
Upper bounds for the number of zeroes for some Abelian integrals
Abelian integrals Weak 16th Hilbert’s Problem limit cycles
2011/2/25
Consider the vector field x′ = −yG(x, y), y′ = xG(x, y), where the set of critical points {G(x, y) = 0} is formed by K straight lines, not passing through the origin and parallel to one or two o...
Redundant Picard-Fuchs system for Abelian integrals
Redundant Picard-Fuchs system Abelian integrals
2010/10/29
We derive an explicit system of Picard-Fuchs differential equations satisfied by Abelian integrals of monomial forms and majorize its coefficients. A peculiar feature of this construction is that the ...