标题： 非线性共振在$ABC$-流中 显示英文标题

标题： Nonlinear resonances in the $ABC$-flow

摘要： 在本文中，我们研究近可积情况下$ABC$流的共振（$C\ll 1$）。这是一个哈密顿系统的一个有趣例子，具有 3/2 自由度，在这种情况下，同一阶数的两个共振同时存在是可能的。得到了共振存在的解析条件。数值上显示最大的$n:1$（$n=1,2,3$）共振存在，它们的能量等于近可积情况下的理论能量。我们在有限运动区域提供了两个最大$n:1$（$n=1,2$）共振的两个分支存在的解析和数值证据。 显示英文摘要

摘要： In this paper we study resonances of the $ABC$-flow in the near integrable case ($C\ll 1$). This is an interesting example of a Hamiltonian system with 3/2 degrees of freedom in which simultaneous existence of two resonances of the same order is possible. Analytical conditions of the resonance existence are received. It is shown numerically that the largest $n:1$ ($n=1,2,3$) resonances exist, and their energies are equal to theoretical energies in the near integrable case. We provide analytical and numerical evidences for existence of two branches of the two largest $n:1$ ($n=1,2$) resonances in the region of finite motion.