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liénard systems

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations
Part of
- Qualitative theory
Maria V. Demina, Claudia Valls
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 6 / December 2020

Published online by Cambridge University Press:

09 January 2020, pp. 3231-3251

Print publication:

December 2020
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We present the complete classification of irreducible invariant algebraic curves of quadratic Liénard differential equations. We prove that these equations have irreducible invariant algebraic curves of unbounded degrees, in contrast with what is wrongly claimed in the literature. In addition, we classify all the quadratic Liénard differential equations that admit a Liouvillian first integral.