This article is cited in 4 papers

Quadratic Differential Equations in Three Variables without Multivalued Solutions: Part I

Adolfo Guillot

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico City 04510, Mexico

Abstract: For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic homogeneous equations in three variables, and begin the classification of those which do not have multivalued solutions.

Keywords: Painlevé property; univalence; semicompleteness; Chazy equation; Riccati equation; Kowalevski exponents.

MSC: 34M55; 34M45; 34M35

Received: May 1, 2018; in final form November 5, 2018; Published online November 11, 2018

Language: English

DOI: 10.3842/SIGMA.2018.122

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ArXiv: 1804.10664