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arXiv · 1011.6090

The geometry of Chazy's homogeneous third-order differential equations

Adolfo Guillot
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Abstract

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 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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Adolfo Guillot. 2012-04-30. The geometry of Chazy's homogeneous third-order differential equations. https://doi.org/10.1619/fesi.55.67

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