一类角度发散在action极限内的Hamilton映射的混沌扩散研究
An investigation of chaotic diffusion in a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action
摘要：
利用扩散方程的解，研究了一类角发散于消失作用极限的Hamilton映射的混沌扩散。该系统是由一个二维映射的变量的行动，$I$，和角度，$θ$和控制的两个控制参数：（i）$ε$，控制系统的非线性，特别是从可积的$ε=0$到不可积的$ε\ne0$的过渡;（ii）$γ$表示的权力的行动在方程定义的角度。对于$ε\ne0$的相空间是混合的，混沌存在于系统中，导致有限扩散的作用，其特征在于扩散方程的解。然后将解析解与数值模拟进行比较，表明两种方法之间存在显著的一致性。
英文摘要：
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, $I$, and angle, $θ$ and controlled by two control parameters: (i) $ε$, controlling the nonlinearity of the system, particularly a transition from integrable for $ε=0$ to non-integrable for $ε\ne0$ and; (ii) $γ$ denoting the power of the action in the equation defining the angle. For $ε\ne0$ the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.
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