Meromorphic functions in a first-order system

2019/06/02 by P. L. Robinson, Robinson, P. L. · 1 citation
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1906.02141

Abstract

We consider the differential equations s' = c⁵ and c' = - s⁵ with initial conditions s(0) = 0 and c(0) = 1. We show that s² c² extends to the reciprocal of the Weierstrass elliptic function with invariants g₂ = 0 and g₃ = 16. We also show that powers of s² c² are the only functions of the form s^m cⁿ that extend meromorphically in the plane.

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