The Phase Space of Chazy’s Equation
نویسنده
چکیده
We study the phase space of Chazy’s equation. 0. Main results In 1979, K. Okamoto constructed the spaces of initial conditions of Painlevé equations, which can be considered as the parametrized spaces of all solutions, including the meromorphic solutions (see [2, 3, 4, 5]) In 1910, Chazy studied Painlevé type equation with third order (see [1]) explicitly given by du dt3 = 2u du dt2 − 3 ( du dt )2 . (1) Here u denotes unknown complex variable. In this paper, we study the phase space of (1) from the viewpoint of its accessible singularities and local index. To do its singularity analysis, at first we transform the equation (1) to the system of differential equations by the canonical transformation. Proposition 0.1. The canonical transformation
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