Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type

Abstract

Some new Hamiltonian systems of quasi-Painlevé type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlevé equations, comparing the irreducible components of the inaccessible divisors arising in the blow-up process, we find bi-rational coordinate changes between some of these systems that give rise to the same global Hamiltonian structure. This scheme thus gives a method for identifying Hamiltonian systems up to bi-rational maps, which is performed in this article for systems of quasi-Painlevé type having singularities that are either square-root type algebraic poles or ordinary poles.

40 pages, 15 figures. Updated version where some figures have been corrected

References in corpus (2)

• Movable algebraic singularities of second-order ordinary differential equations
• Spaces of initial conditions for quartic Hamiltonian systems of Painlevé and quasi-Painlevé type