Two flows Kowalevski top as the full genus two Jacobi’s inversion problem and Sp(4, R ) lie group structure

By using the first and second flows of Kowalevski top, we can make top into two which has time variales. Then show that equations become those full genus Jacobi inversion problem. In addition to Lax pair for flow, costruct flow. Using flows, Lie group structure these pairs is Sp(4,$\mathbb{R}$) $\cong$ SO(3,2). Through conclude hyperelliptic function