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Integrable systems in the plane with center type linear part

100%

Chavarriga J.

Applicationes Mathematicae

1993-1995

tom 22

nr 2

285-309

We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.

A class of integrable polynomial vector fields

100%

Chavarriga J.

Applicationes Mathematicae

1995-1996

tom 23

nr 3

339-350

We study the integrability of two-dimensional autonomous systems in the plane of the form $\dotx=-y+X_s(x,y)$, $\doty=x+Y_s(x,y)$, where X_s(x,y) and Y_s(x,y) are homogeneous polynomials of degree s with s≥2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable $(x^2+y^2)^{s/2-1}$ with coefficients being functions of tan^{−1}(y/x).

Ograniczanie wyników

2 Applicationes Mathematicae

2 Chavarriga J.

1 1995

1 1994

Wyniki wyszukiwania

Integrable systems in the plane with center type linear part

A class of integrable polynomial vector fields