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| A SUFFICIENT AND NECESSARY CONDITION OF THE EXISTENCE TO A DOUBLE BUN TYPE SEPARATRIX CYCLE FOR AXIAL SYMMETRY CUBIC SYSTEM | |
| 作者姓名： | 沈伯骞 沈洁 |
| 摘 要： | 1 IntroductionThere is almost no other type of algebraic curve which may be able tofOrm a separatrix cyc1e containing a fOcus fOr quadratic systern except para-bola, hyperbo1a, ellipse, parabola and straight line, two half lines and relativeequatorial arc, a class of cubic curve and two classes of quartic curve (see 1]for details). However, besides of these, there are many other types of algebraiccurves which may be able to fOrm a separatrix cycle fOr cubic system, fOr ex-ample, double foli… |
A SUFFICIENT AND NECESSARY CONDITION OF THE EXISTENCE TO A DOUBLE BUN TYPE SEPARATRIX CYCLE FOR AXIAL SYMMETRY CUBIC SYSTEM |
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| Abstract: | A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is also given. |
| Keywords: | double bun curve separatrix cycle topological structure |