On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
The authors consider a class of finite-dimensional integral systems having the weak Kowalevski-Painlevé property, which generalizes the notion of algebraic complete integrability. The authors allow that their real invariant \(N\)-dimensional Liouville tori are extended to \(N\)-dimensional complex analytic nonlinear subvarieties of Abelian tori of dimension \(g\geq n\), so-called strata. Here, the nonlinearity means that such subvarieties are not complex Abelian groups. Moreover, the authors require that on universal coverings of the Abelian tori there exists coordinates \(\varphi_1,\dots, \varphi_g\) such that under the Hamiltonian flow, \(\varphi_1,\dots, \varphi_N\) change linearly in time \(t\), whereas the rest of the coordinates are analytic functions of the former. Some model examples are considered, such as the hierarchy of integrable generalizations of the Hénon-Heiles and the Neumann systems.
scientific article; zbMATH DE number 1506490