论文标题
二维周期系统的不变摩托
Invariant Tori of a Two Dimensional Periodic System with the Linear-Cubic Unperturbed Part
论文作者
论文摘要
研究了具有较小的非负参数的普通微分方程的两个时间周期系统，即具有快速和缓慢的时间的参数。这些系统的右侧相对于相位变量连续三倍，并且相应的不受干扰的系统是自主，保守的，并且具有九个平衡点。对于不明确取决于参数的扰动系统，我们获得了产生的条件，即初始系统具有一定数量的二维不变表面，每个参数值和此类表面的公式为每个足够小的参数值和此类表面的公式。研究了一类具有七个不变表面的系统，该系统封闭了平衡点的不同配置，作为我们方法应用的一个示例。
Two classes of time-periodic systems of ordinary differential equations with a small nonnegative parameter, those with fast and slow time, are studied. Right-hand sides of these systems are three times continuously differentiable with respect to phase variables and the parameter, the corresponding unperturbed systems are autonomous, conservative and have nine equilibrium points. For the perturbed systems, which do not depend on the parameter explicitly, we obtain the conditions yielding that the initial system has a certain number of two-dimensional invariant surfaces homeomorphic to a torus for each sufficiently small values of parameter and the formulas of such surfaces. A class of systems with seven invariant surfaces enclosing different configurations of equilibrium points is studied as an example of applications of our method.
