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引用次数: 0
摘要
本文研究了具有$0:1:-1$原点共振奇点的三维多项式系统$x\到x， $ y\到\ α y， $ z \到\ α ^{-1}z$的变换群的时间可逆性和不变量。提出了一种在参数空间中求时间可逆系统集的Zariski闭包的算法。讨论了上述群的时间可逆性与不变量的相互关系。
Time-Reversibility and Ivariants of Some 3-dim Systems
We study time-reversibility and invariants of the group of transformations $x\to x, \ y\to \alpha y, \ z \to \alpha ^{-1}z$ for three-dimensional polynomial systems with $0:1:-1$ resonant singular point at the origin. An algorithm to find the Zariski closure of the set of time-reversible systems in the space of parameters is proposed. The interconnection of time-reversibility and invariants of the group mentioned above is discussed.
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