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DARBOUX POLYNOMIALS AND ALGEBRAIC INTEGRABILITY OF THE CHEN SYSTEM

TINGHUA LÜ

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China

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and

XIANG ZHANG

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China

Author for correspondence.

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https://doi.org/10.1142/S0218127407018725Cited by:22 (Source: Crossref)

Abstract

In this paper, we characterize all the Darboux polynomials of the Chen system, , and prove that the system is not algebraic integrability. For proving the results, we use the weight homogeneous polynomials and the method of characteristics.

Keywords:

References

G. Chen and T. Ueta, Int. J. Bifurcation and Chaos 9, 1465 (1999). Link, Web of Science, Google Scholar
G. Darboux, Bull. Sci. Math. 2ème Série 2, 60 (1878). Google Scholar
A. R. Forsyth , Theory of Differential Equations ( Cambridge University Press , Cambridge , 1900 ) . Google Scholar
J. P. Jouanolou , Equations de Pfaff algébriques , Lecture Notes in Mathematics 708 ( Springer , NY , 1979 ) . Crossref, Google Scholar
J. Llibre and X. Zhang, J. Math. Phys. 43, 1622 (2002), DOI: 10.1063/1.1435078. Crossref, Web of Science, Google Scholar
J. Llibre and C. Valls, J. Phys. A: Math. Gen. 38, 2681 (2005), DOI: 10.1088/0305-4470/38/12/010. Crossref, Google Scholar
J. Moulin-Ollagnier, Bull. Sci. Math. 121, 463 (1997). Web of Science, Google Scholar
J. Moulin-Ollagnier, Bull. Sci. Math. 123, 437 (1999). Crossref, Web of Science, Google Scholar
H. Poincaré, Rendiconti del Circolo Matematico di Palermo 5, 161 (1891). Crossref, Google Scholar
X. Zhang, J. Phy. A: Math. Gen. 33, 5137 (2000). Crossref, Google Scholar