Liouvillian First Integrals of Differential Equations

@inproceedings{Singer1988LiouvillianFI,
  title={Liouvillian First Integrals of Differential Equations},
  author={M. Singer},
  booktitle={ISSAC},
  year={1988}
}
  • M. Singer
  • Published in ISSAC 1988
  • Mathematics, Computer Science
Liouvillian functions are functions that are built up from rational functions using exponentiation, integration, and algebraic functions. We show that if a system of differential equations has a generic solution that satisfies a liouvillian relation, that is, there is a liouvillian function of several variables vanishing on the curve defined by this solution, then the system has a liouvillian first integral, that is a nonconstant liouvillian function that is constant on solution curves in some… Expand
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Holomorphic foliations with Liouvillian first integrals
Rational integration of the Lotka–Volterra system
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