A class of integrable polynomial vector fields
Applicationes Mathematicae (1995)
- Volume: 23, Issue: 3, page 339-350
- ISSN: 1233-7234
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topChavarriga, Javier. "A class of integrable polynomial vector fields." Applicationes Mathematicae 23.3 (1995): 339-350. <http://eudml.org/doc/219136>.
@article{Chavarriga1995,
abstract = {We study the integrability of two-dimensional autonomous systems in the plane of the form $=-y+X_s(x,y)$, $=x+Y_s(x,y)$, where Xs(x,y) and Ys(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).},
author = {Chavarriga, Javier},
journal = {Applicationes Mathematicae},
keywords = {integrable systems in the plane; center-focus problem; particular solutions; integrability; two-dimensional autonomous systems; homogeneous polynomials},
language = {eng},
number = {3},
pages = {339-350},
title = {A class of integrable polynomial vector fields},
url = {http://eudml.org/doc/219136},
volume = {23},
year = {1995},
}
TY - JOUR
AU - Chavarriga, Javier
TI - A class of integrable polynomial vector fields
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 3
SP - 339
EP - 350
AB - We study the integrability of two-dimensional autonomous systems in the plane of the form $=-y+X_s(x,y)$, $=x+Y_s(x,y)$, where Xs(x,y) and Ys(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).
LA - eng
KW - integrable systems in the plane; center-focus problem; particular solutions; integrability; two-dimensional autonomous systems; homogeneous polynomials
UR - http://eudml.org/doc/219136
ER -
References
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- [6] D. Schlomiuk, Algebraic and geometric aspects of the theory of polynomial vector fields, in: Bifurcations and Periodic Orbits of Vector Fields, Kluwer Acad. Publ., 1993, 429-467. Zbl0790.34031
- [7] S. Shi, A method of constructing cycles without contact around a weak focus, J. Differential Equations 41 (1981), 301-312. Zbl0442.34029
- [8] H. Żołądek, On a certain generalization of Bautin's Theorem, preprint, Institute of Mathematics, University of Warsaw, 1991. Zbl0838.34035
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