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Transactions of the American Mathematical Society

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Geometric properties of homogeneous vector fields of degree two in $ {\bf R}\sp{3}$


Author: M. Izabel T. Camacho
Journal: Trans. Amer. Math. Soc. 268 (1981), 79-101
MSC: Primary 58F09; Secondary 34D30
MathSciNet review: 628447
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Abstract: In the space of homogeneous polynomial vector fields of degree two, those that project on Morse-Smale vector fields on $ {S^2}$ by the Poincaré central projection form a generic subset. The classification of those vector fields on $ {S^2}$ without periodic orbits is given and applications to the study of local actions of the affine group of the line are derived.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0628447-1
Article copyright: © Copyright 1981 American Mathematical Society