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

TL;DR

This paper investigates a specific class of complex differential equations in three variables, aiming to classify those that do not produce multivalued solutions, which is key for understanding their solution structure.

Contribution

It introduces a classification of autonomous, first-order, quadratic homogeneous equations in three variables that lack multivalued solutions.

Findings

Identifies conditions for non-multivalued solutions

Provides a framework for classifying such equations

Lays groundwork for further analysis in complex differential equations

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.