论文标题
平面多项式系统的关键时期数量的新下限
New lower bound for the number of critical periods for planar polynomial systems
论文作者
论文摘要
在本文中，我们构建了两类的平面多项式哈密顿系统，其起源为中心，并获得这些系统的关键时期数量的下限。对于$ n $的多项式潜在系统，我们为关键时期数量提供$ n-2 $的下限，对于$ n $的多项式系统，当$ n^2/2+n-5/2 $的下限$ n^2/2+n-5/2 $时，当$ n $是奇数且$ n^2/2-2 $时，$ n^2/2-2 $何时适合关键时期的数量。据我们所知，这些下限是新的，此外，后者是现有结果到主要术语的两倍。
In this paper, we construct two classes of planar polynomial Hamiltonian systems having a center at the origin, and obtain the lower bounds for the number of critical periods for these systems. For polynomial potential systems of degree $n$, we provide a lower bound of $n-2$ for the number of critical periods, and for polynomial systems of degree $n$, we acquire a lower bound of $n^2/2+n-5/2$ when $n$ is odd and $n^2/2-2$ when $n$ is even for the number of critical periods. To the best of our knowledge, these lower bounds are new, moreover the latter one is twice the existing results up to the dominant term.
