| Some Properties of Homogeneous Vector Fields |
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| 作者姓名： | 盛平兴 |
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| 摘 要： | Letbox)=(QI(x),Qz(x),Qz(x))(xER')beapolynomialnomogeneousvectorfield.ItinducesatangentvectorfieldonS'.denotedbyLetybeaclosedorbitofQ7'(x)onSZ.DefineaconewnicniscanedaninvariantconeofQ(x)inR'generatedbyQ700.Colenlanl']andSharipovi'lconsideredsomeproperties…
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| 收稿时间： | 16 April 1997 |
Some properties of homogeneous vector fields |
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| Pingxing Sheng.Some Properties of Homogeneous Vector Fields[J].Journal of Shanghai University(English Edition),1997,1(3):191-195. |
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| Authors: | Pingxing Sheng |
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| Institution: | College of Sciences |
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| Abstract: | For planar analytic homogcneous vector fields, the existence of periodic orbits and the noncxistence of limit sets arc verilied. It is concluded that spacial analytic homlogencous vector tleld of order in has no limit sets for any m>1. Similar results arc extended to highel-dimensional polynomial homogeneous vector fields under certain conditions. |
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| Keywords: | homogeneous vector field induced tangcnt vector held Hairy Ban theorem invariant cone qnalitative analysis closed orbits and limit sets |
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