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Open AccessArticle

Meromorphic Non-Integrability of Several 3D Dynamical Systems

by Kaiyin Huang 1,2, Shaoyun Shi 1,2 and Wenlei Li 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
Entropy 2017, 19(5), 211; https://doi.org/10.3390/e19050211
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)
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
MDPI and ACS Style

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

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