The Liouvillian Integrability of Several Oscillators-Reference-Cited by-同舟云学术

The Liouvillian Integrability of Several Oscillators

Published:2019-05 Issue:05 Volume:29 Page:1950069
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Giné Jaume¹,Valls Claudia²

Affiliation:

1. Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain

2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049-001, Lisboa, Portugal

Abstract

In this paper, we characterize all the Liouvillian first integrals of a cubic polynomial differential system that contains the van der Pol and the Duffing oscillators. It is also shown that the centers correspond to the Liouville integrable cases.

Funder

Ministerio de Economía, Industria y Competitividad, Gobierno de España

Agència de Gestió d'Ajuts Universitaris i de Recerca

Fundação para a Ciência e a Tecnologia

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021812741950069X

Reference7 articles.

1. Nondegenerate and Nilpotent Centers for a Cubic System of Differential Equations

2. Local analytic integrability for nilpotent centers

3. Essential variables in the integrability problem of planar vector fields

4. Liénard Equation and Its Generalizations

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