# Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Li\'enard equation

@article{Choudhury2016ChielliniIC, title={Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Li\'enard equation}, author={Anindya Ghose Choudhury and Partha Guha}, journal={arXiv: Exactly Solvable and Integrable Systems}, year={2016} }

Using a novel transformation involving the Jacobi Last Multiplier (JLM) we derive an old integrability criterion due to Chiellini for the Li\'enard equation. By combining the Chiellini condition for integrability and Jacobi's Last Multiplier the Lagrangian and Hamiltonian of the Li\'enard equation is derived. We also show that the Kukles equation is the only equation in the Li\'enard family which satisfies both the Chiellini integrability and the Sabatini criterion for isochronicity conditions… Expand

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