Action variables of the Kovalevskaya top

An explicit formula for the action variables of the Kovalevskaya top as Abelian integrals of the third kind on the Kovalevskaya curve is found. The linear system of differential equations of Picard–Fuchs type, describing the dependence of these variables on the integrals of the Kovalevskaya system, is presented in explicit form. The results are based on the formula for the actions derived by S.P. Novikov and A.P. Veselov within the theory of algebro-geometric Poisson brackets on the universal bundle of hyperelliptic Jacobians.