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Entropy 2017, 19(5), 211; doi:10.3390/e19050211

Meromorphic Non-Integrability of Several 3D Dynamical Systems

1,2
,
1,2
and
1,3,*
1
School of Mathematics, Jilin University, Changchun 130012, China
2
State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, China
3
Beijing Computational Science Research Center, Haidian District, Beijing 100094, China
*
Author to whom correspondence should be addressed.
Academic Editor: Gunnar Pruessner
Received: 4 March 2017 / Revised: 17 April 2017 / Accepted: 29 April 2017 / Published: 10 May 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
View Full-Text   |   Download PDF [279 KB, uploaded 19 May 2017]

Abstract

In this paper, we apply the differential Galoisian approach to investigate the meromorphic non-integrability of a class of 3D equations in mathematical physics, including Nosé–Hoover equations, the Lü system, the Rikitake-like system and Rucklidge equations, which are well known in the fields of molecular dynamics, chaotic theory and fluid mechanics, respectively. Our main results show that all these considered systems are, in fact, non-integrable in nearly all parameters. View Full-Text
Keywords: differential Galois theory; first integrals; meromorphic non-integrability differential Galois theory; first integrals; meromorphic non-integrability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Huang, K.; Shi, S.; Li, W. Meromorphic Non-Integrability of Several 3D Dynamical Systems. Entropy 2017, 19, 211.

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