Darboux integrability for the Rössler system

Jaume Llibre; Xiang Zhang

doi:https://doi.org/10.1142/S0218127402004474

Darboux integrability for the Rössler system

Jaume Llibre, Xiang Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

16 Citations (Scopus)

Abstract

In this note we characterize all generators of Darboux polynomials of the Rössler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. As a corollary we prove that the Rössler system is not algebraically integrable, and that every rational first integral is a rational function in the variable x2+y2+2z. Moreover, we characterize the topological phase portrait of the Darboux integrable Rössler system.

Original language	English
Pages (from-to)	421-428
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	12
DOIs	https://doi.org/10.1142/S0218127402004474
Publication status	Published - 1 Jan 2002

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title = "Darboux integrability for the R{\"o}ssler system",

abstract = "In this note we characterize all generators of Darboux polynomials of the R{\"o}ssler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. As a corollary we prove that the R{\"o}ssler system is not algebraically integrable, and that every rational first integral is a rational function in the variable x2+y2+2z. Moreover, we characterize the topological phase portrait of the Darboux integrable R{\"o}ssler system.",

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AU - Zhang, Xiang

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N2 - In this note we characterize all generators of Darboux polynomials of the Rössler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. As a corollary we prove that the Rössler system is not algebraically integrable, and that every rational first integral is a rational function in the variable x2+y2+2z. Moreover, we characterize the topological phase portrait of the Darboux integrable Rössler system.

AB - In this note we characterize all generators of Darboux polynomials of the Rössler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. As a corollary we prove that the Rössler system is not algebraically integrable, and that every rational first integral is a rational function in the variable x2+y2+2z. Moreover, we characterize the topological phase portrait of the Darboux integrable Rössler system.

U2 - https://doi.org/10.1142/S0218127402004474

DO - https://doi.org/10.1142/S0218127402004474

M3 - Article

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EP - 428

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