Some Elements about Ordinary Differential Equations
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This chapter is merely devoted to recalling usual notation and elementary results on ordinary differential equations in the complex domain. We give the fundamental existence theorem for Cauchy problems (Sect. 1.1). We detail the main differences between solutions of linear versus nonlinear ODEs, when the question of their analytic continuation is considered (Sect. 1.2). Finally we provide a short introduction to Painlevé equations (Sect. 1.3).
KeywordsOrdinary Differential Equation Riemann Surface Meromorphic Function Algebraic Differential Equation Linear Ordinary Differential Equation
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