A tower of genus two curves related to the Kowalewski top

Several curves of genus 2 are known, such that the equations of motion of t he Kowalewski top are linearized on their Jacobians. One can expect from tr anscendental approaches via solutions of equations of motion in theta-funct ions, that their Jacobians are isogeneous. The paper focuses on two such cu rves: Kowalewski's and that of Bobenko-Reyman-Semenov-Tian-Shansky, the lat ter arising from the solution of the problem by the method of spectral curv es. An isogeny is established between the Jacobians of these curves by pure ly algebraic means, using Richelot's transformation of a genus 2 curve. It is shown that this isogeny respects the Hamiltonian flows. The two curves a re completed into an infinite tower of genus 2 curves with isogeneous Jacob ians.