论文标题
关于带有分离质交叉的哈密顿系统扰动的相变
On the phase change for perturbations of Hamiltonian systems with separatrix crossing
论文作者
论文摘要
我们研究了一般（不一定是哈密顿量）对汉密尔顿系统的扰动的角变量（相）的演变，该系统具有一种自由度，接近不受干扰的系统的分离。为此，我们使用订单2的平均系统。我们获得了分离阶附近订单2平均系统准确性的估计值，并使用这些估算值证明当扰动系统的溶液的解决方案分离不受干扰的系统时（当扰动是汉密尔顿时，该公式是汉密尔顿时的公式）。作为该公式的应用，我们表明在V.I.提出的分离越过后，将捕获概率的两个自然定义是捕获概率的两个自然定义。 Arnold和D.V. Anosov导致相同的公式以达到此概率。
We study the evolution of angular variable (phase) for general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. To this end, we use averaged system of order 2. We obtain estimates for the accuracy of order 2 averaged system near separatrices and use these estimates to prove a formula for the phase change when solutions of the perturbed system approach separatrices of the unperturbed system (such formula is known when the perturbation is Hamiltonian). As an application of this formula, we show that two natural definitions of probability of capture into different domains after separatrix crossing proposed by V.I. Arnold and D.V. Anosov lead to the same formula for this probability.
