Abstract
Abstract
We describe the quasi-Painlevé property of a system of ordinary differential equations in terms of a global Hamiltonian structure on an analogue of Okamoto’s space of initial conditions for the Painlevé equations. In the quasi-Painlevé case, the Hamiltonian structure is with respect to a two-form which is allowed to have certain zeroes on the surfaces forming the space of initial conditions, as opposed to holomorphic symplectic forms in the case of the Painlevé equations. We provide the spaces and Hamiltonian structures for several known quasi-Painlevé equations and also for a new example, which we prove to have the quasi-Painlevé property via the Hamiltonian structure and construction of an appropriate auxiliary function which remains bounded on solutions.
Funder
Japan Society for the Promotion of Science
Narodowe Centrum Nauki
European Regional Development Fund
Ministerio de Ciencia e Innovación
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics