TY - GEN

T1 - First Integrals of a Cubic System of Differential Equations

AU - Kadyrsizova, Zhibek

AU - Romanovski, Valery G.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - We study polynomial systems of differential equations of the form X = x+p(x,y), y = -3y+q(x,y), (1) where p(x,y) and q(x,y) are homogeneous polynomials of degree three. In [1] the linearizability problem for this system has been studied. In many cases considered in [1] the construction of linearizing transformations requires knowledge of first integrals. In [2] it has been proved that such integrals exist. In the present paper we find the explicit expressions for the integrals. It allows to obtain the explicit formulas for the corresponding linearizing transformations of [1].

AB - We study polynomial systems of differential equations of the form X = x+p(x,y), y = -3y+q(x,y), (1) where p(x,y) and q(x,y) are homogeneous polynomials of degree three. In [1] the linearizability problem for this system has been studied. In many cases considered in [1] the construction of linearizing transformations requires knowledge of first integrals. In [2] it has been proved that such integrals exist. In the present paper we find the explicit expressions for the integrals. It allows to obtain the explicit formulas for the corresponding linearizing transformations of [1].

KW - integrability

KW - ordinary differential equations

KW - the center and linearizability problems

UR - http://www.scopus.com/inward/record.url?scp=85006226821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006226821&partnerID=8YFLogxK

U2 - 10.1063/1.3046241

DO - 10.1063/1.3046241

M3 - Conference contribution

AN - SCOPUS:85006226821

T3 - AIP Conference Proceedings

SP - 104

EP - 111

BT - 7th International Summer School/Conference "Let's Face Chaos Through Nonlinear Dynamics" - Dedicated to the 65th Birthday of Professor Giulio Casati

A2 - Romanovski, Valery G.

A2 - Robnik, Marko

PB - American Institute of Physics Inc.

T2 - 7th International Summer School/Conference "Let's Face Chaos Through Nonlinear Dynamics"

Y2 - 29 June 2008 through 13 July 2008

ER -