1. The limit set of trajectory in quasi-homogeneous system in ℝ.
- Author
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Huang, Jianfeng and Zhao, Yunlin
- Subjects
- *
TRAJECTORY optimization , *FIXED point theory , *ORBIT method , *HOMOGENEOUS spaces , *MANIFOLDS (Mathematics) , *MATHEMATICAL singularities , *SET theory - Abstract
In this article, we study the limit set of trajectory in three-dimensional quasi-homogeneous system. For the trajectory which is close to a singular curve, we show that either it approaches a fixed point or infinity, or it oscillates. Moreover, an oscillating example is given. The behaviour of trajectory which is near a closed orbit is also studied. At the end, we classify the integral manifolds of the system with isolated singularities. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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