Morphisms and Inverse Problems for Darboux Integrating Factors
نویسندگان
چکیده
Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we discuss in detail one particular class of morphisms related to finite reflection groups. The results indicate that degeneracies for the underlying curve generally impose restrictions on the nontrivial vector fields which admit a given integrating
منابع مشابه
Morphisms and Inverse Problems
In order to investigate polynomial vector fields admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the affine plane. In particular, such morphisms may be used to remove degeneracies of the underlying curve. Our main result states that the space of vector fields admitting a prescribed Darboux integrating factor modulo a well understood subspace ...
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