### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 122, 46 pages      arXiv:1804.10664      https://doi.org/10.3842/SIGMA.2018.122

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

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

Received May 01, 2018, in final form November 05, 2018; Published online November 11, 2018

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.

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

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