On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n

Jaume Llibre; Clàudia Valls

doi:https://doi.org/10.1142/S0219199717500456

On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n

Jaume Llibre, Clàudia Valls

Department of Mathematics

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Abstract

© 2018 World Scientific Publishing Company. We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1 2=i=1dp12 + V (q 1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.

Original language	English
Article number	1750045
Journal	Communications in Contemporary Mathematics
Volume	20
DOIs	https://doi.org/10.1142/S0219199717500456
Publication status	Published - 1 Dec 2018

Keywords

Darboux first integrals
Darboux polynomials
Hamiltonian systems
exponential factors
polynomial integrability
weight-homogenous differential systems

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https://doi.org/10.1142/S0219199717500456

https://ddd.uab.cat/record/221335

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title = "On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n",

abstract = "{\textcopyright} 2018 World Scientific Publishing Company. We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1 2=i=1dp12 + V (q 1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.",

keywords = "Darboux first integrals, Darboux polynomials, Hamiltonian systems, exponential factors, polynomial integrability, weight-homogenous differential systems",

author = "Jaume Llibre and Cl{\`a}udia Valls",

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AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2018/12/1

Y1 - 2018/12/1

N2 - © 2018 World Scientific Publishing Company. We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1 2=i=1dp12 + V (q 1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.

AB - © 2018 World Scientific Publishing Company. We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1 2=i=1dp12 + V (q 1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.

KW - Darboux first integrals

KW - Darboux polynomials

KW - Hamiltonian systems

KW - exponential factors

KW - polynomial integrability

KW - weight-homogenous differential systems

U2 - https://doi.org/10.1142/S0219199717500456

DO - https://doi.org/10.1142/S0219199717500456

M3 - Article

VL - 20

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

M1 - 1750045

ER -

On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n

Abstract

Keywords

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