In this paper we present sufficient conditions guaranteeing that a polynomial autonomous system has a periodic orbit /spl Gamma//sub 1/ passing through some point x/sub 1/ provided there is another point x/sub 2/ which is contained in some periodic orbit /spl Gamma//sub 2/. We consider two cases: the case of equal minimal periods and the case of nonequal periods. Our approach described for periodic orbits is applied to polynomial autonomous systems with homoclinic orbits and heteroclinic orbits as well. One example is examined.
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机译：在本文中，我们提出了充分的条件，以确保多项式自治系统具有通过某点x / sub 1 /的周期轨道/ spl Gamma // sub 1 /，前提是在某个周期中包含另一个点x / sub 2 /轨道/ spl Gamma // sub 2 /。我们考虑两种情况：最小周期相等的情况和不相等周期的情况。我们针对周期轨道描述的方法也应用于具有同斜轨道和异斜轨道的多项式自治系统。研究了一个例子。
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