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DARBOUX INTEGRABILITY FOR THE RÖSSLER SYSTEM

JAUME LLIBRE

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 - Bellaterra, Barcelona, Spain

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and

XIANG ZHANG

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P.R. China

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https://doi.org/10.1142/S0218127402004474Cited by:19 (Source: Crossref)

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.

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