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

56 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

Access to Document

10.1063/1.1435078

Fingerprint Dive into the research topics of 'Invariant algebraic surfaces of the Lorenz system'. Together they form a unique fingerprint.

Cite this

@article{c58b0beec0d140eea499eb45d5198eab,

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.",

author = "Jaume Llibre and Xiang Zhang",

year = "2002",

month = mar,

day = "1",

doi = "10.1063/1.1435078",

language = "English",

volume = "43",

pages = "1622--1645",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

number = "3",

}

TY - JOUR

T1 - Invariant algebraic surfaces of the Lorenz system

AU - Llibre, Jaume

AU - Zhang, Xiang

PY - 2002/3/1

Y1 - 2002/3/1

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.

U2 - 10.1063/1.1435078

DO - 10.1063/1.1435078

M3 - Article

VL - 43

SP - 1622

EP - 1645

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

ER -