Volume 24, Issue 4, September 2017, Pages 473 - 494
On the Darboux integrability of a three–dimensional forced–damped differential system
Authors
Jaume Llibre
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain.jllibre@mat.uab.cat
Regilene Oliveira
Departamento de Matemática, ICMC, Universidade de São Paulo, Av. Trabalhador São-carlense, 400, 13566-590, São Carlos, SP, Brazil.regilene@icmc.usp.br
Claudia Valls
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049-001, Lisboa, Portugal.cvalls@math.ist.utl.pt
Received 10 September 2016, Accepted 23 May 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1375686How to use a DOI?
- Keywords
- Invariant algebraic surfaces; exponential factors; first integral; four-scroll chaotic system
- Abstract
In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. In this paper we study the opposite to its chaotic motion, i.e. its integrability, mainly the existence of polynomial, rational and Darboux first integrals through the analysis of its invariant algebraic surfaces and its exponential factors.
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Jaume Llibre AU - Regilene Oliveira AU - Claudia Valls PY - 2021 DA - 2021/01/06 TI - On the Darboux integrability of a three–dimensional forced–damped differential system JO - Journal of Nonlinear Mathematical Physics SP - 473 EP - 494 VL - 24 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1375686 DO - 10.1080/14029251.2017.1375686 ID - Llibre2021 ER -