Geometric approach for quasi-Painlevé Hamiltonian systems

Abstract: We present some new Hamiltonian systems of quasi-Painlevé type and their Okamoto's spaces of initial conditions. The geometric approach was introduced originally for the identification problem of Painlevé equations, comparing the irreducible components of the inaccessible divisors introduced in the blow-ups to obtain the space of initial conditions. Using this method, we find bi-rational coordinate changes between some of the systems we introduce, giving rise to a global symplectic structure for these systems. This scheme thus allows us to identify (quasi-)Painlevé Hamiltonian systems up to bi-rational symplectic maps, performed here for systems with solutions having movable singularities that are either square-root type algebraic poles or ordinary poles.

complex variablesdynamical systems

Audience: researchers in the topic

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