Funkcialaj Ekvacioj
Print ISSN : 0532-8721
The Geometry of Chazy's Homogeneous Third-Order Differential Equations
Adolfo Guillot
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2012 年 55 巻 1 号 p. 67-87

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Chazy studied a family of homogeneous third-order autonomous differential equations. They are those, within a certain class, admitting exclusively single-valued solutions. Each one of these equations yields a polynomial vector field in complex three-dimensional space. For almost all of these vector fields, the Zariski closure of a generic orbit yields an affine surface endowed with a holomorphic vector field that has exclusively single-valued solutions. We classify these surfaces and relate this classification to recent results of Rebelo and the author.
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© 2012 by the Division of Functional Equations, The Mathematical Society of Japan
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