Invariant algebraic surfaces of the Lorenz system

Jaume Llibre; Xiang Zhang

doi:10.1063/1.1435078

Invariant algebraic surfaces of the Lorenz system

Jaume Llibre, Xiang Zhang

Department of Mathematics

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

57 Citations (Scopus)

Abstract

In this paper we provide a complete classification of the Darboux invariants, of the irreducible Darboux polynomials, of the rational first integrals and of the algebraic integrability for the classical Lorenz system ẋ = s(y - x), ẏ = rx - y - xz, ż = - bz + xy. In the proofs, we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. © 2002 American Institute of Physics.

Original language	English
Pages (from-to)	1622-1645
Journal	Journal of Mathematical Physics
Volume	43
Issue number	3
DOIs	https://doi.org/10.1063/1.1435078
Publication status	Published - 1 Mar 2002

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title = "Invariant algebraic surfaces of the Lorenz system",

abstract = "In this paper we provide a complete classification of the Darboux invariants, of the irreducible Darboux polynomials, of the rational first integrals and of the algebraic integrability for the classical Lorenz system ẋ = s(y - x), ẏ = rx - y - xz, {\.z} = - bz + xy. In the proofs, we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. {\textcopyright} 2002 American Institute of Physics.",

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N2 - In this paper we provide a complete classification of the Darboux invariants, of the irreducible Darboux polynomials, of the rational first integrals and of the algebraic integrability for the classical Lorenz system ẋ = s(y - x), ẏ = rx - y - xz, ż = - bz + xy. In the proofs, we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. © 2002 American Institute of Physics.

AB - In this paper we provide a complete classification of the Darboux invariants, of the irreducible Darboux polynomials, of the rational first integrals and of the algebraic integrability for the classical Lorenz system ẋ = s(y - x), ẏ = rx - y - xz, ż = - bz + xy. In the proofs, we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. © 2002 American Institute of Physics.

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