On the algebraic non-integrability of the Halphen system
Andrzej J.~Maciejewski (Institute of Astronomy, N. Copernicus, University, Chopina 12-18, 87-100 Toru\'n, Poland), Jean-Marie Strelcyn, (D\'epartement de Math\'ematiques, Universit\'e de Rouen,76821 Mont Saint, Aignan Cedex, France, URA CNRS 1378)
TL;DR
This paper proves that the Halphen system of differential equations does not possess any non-trivial rational first integrals, indicating its algebraic non-integrability.
Contribution
It establishes the algebraic non-integrability of the Halphen system by proving the absence of non-trivial rational first integrals.
Findings
Halphen system has no non-trivial rational first integrals
The result implies algebraic non-integrability of the system
Provides a rigorous proof of non-integrability
Abstract
It is proved that the Halphen system of ordinary differential equations has no non-trivial rational first integrals.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons · Advanced Topics in Algebra