Volume 20, Issue 4, December 2013, Pages 475 - 479
On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems
Authors
Guillaume Chèze
Institut de Mathématiques de Toulouse, Université Paul Sabatier Toulouse 3, CNRS UMR 5219 MIP Bât 1R3, 31 062 TOULOUSE cedex 9, France,guillaume.cheze@math.univ-toulouse.fr
Thomas Cluzeau
Université de Limoges ; CNRS ; XLIM UMR 7252 ; DMI 123 avenue Albert Thomas, 87 060 LIMOGES cedex, France,thomas.cluzeau@xlim.fr
Received 8 June 2013, Accepted 18 September 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.868260How to use a DOI?
- Keywords
- polynomial vector fields; first integrals; invariant algebraic curves; Liénard polynomial differential systems
- Abstract
We consider generalized Liénard polynomial differential systems of the form ẋ = y, ẏ = -g(x) - f (x) y, with f (x) and g(x) two polynomials satisfying deg(g) ≤ deg(f). In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In this letter, we give a direct and shorter proof of this result.
- Copyright
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Guillaume Chèze AU - Thomas Cluzeau PY - 2021 DA - 2021/01/06 TI - On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems JO - Journal of Nonlinear Mathematical Physics SP - 475 EP - 479 VL - 20 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.868260 DO - 10.1080/14029251.2013.868260 ID - Chèze2021 ER -