非自治标准非扭转映射
Non-autonomous standard nontwist map
AI总结：
该研究针对调制系数线性递增的非自治标准非扭转映射，探究无剪切快照环面的演化，明确混沌转变关键参数与迭代时间的幂律关系，揭示时变参数下混沌路径的影响因素及额外输运效应。
摘要：
保面积非扭转映射会局部违反扭转条件，从而产生无剪切曲线。非扭转系统出现在等离子体物理、气候物理、经典力学等不同物理场景中。标准非扭转映射（standard nontwist map, SNM）可刻画非扭转映射的通用性质，该映射依赖对流参数$a$和调制系数$b$。\n受非自治系统研究思路启发，我们研究了调制系数线性递增的标准非扭转映射（SNM），并探究了相空间中一群初始位于初始态无剪切不变曲线（被称为无剪切快照环面）的点的演化规律。\n参数恒定的SNM中，根据参数空间的区域不同，会出现不同的周期轨道碰撞/湮灭场景，最终引发全局输运；而时变参数的SNM与之不同，其通往混沌的路径不仅与$(a,b)$参数空间中的路径相关，还与参数$b_n$的演化场景有关。\n本研究确定了混沌转变的关键参数与迭代时间之间的幂律关系。此外，我们分析了混沌转变过程中的系统可逆性，并证实了额外输运现象的存在：参数变化会改变扩散系数。
英文摘要：
Area-preserving nontwist maps locally violate the twist condition, giving rise to shearless curves. Nontwist systems appear in different physical contexts, such as plasma physics, climate physics, classical mechanics, etc. Generic properties of nontwist maps are captured by the standard nontwist map, which depends on a convection parameter $a$ and a modulation coefficient $b$. In the spirit of non-autonomous systems, we consider the standard nontwist map (SNM) with a linearly increasing modulation coefficient, and we investigate the evolution of an ensemble of points on the phase space that initially lies on the shearless invariant curve in the initial state, called shearless snapshot torus. Differently from the SNM with constant parameters -- where we can see different scenarios of collision/annihilation of periodic orbits leading to global transport, depending on the region in the parameter space -- for the SNM with time-dependent parameters, the route to chaos is not only related to the path in the $(a, b)$ parameter space, but also to the scenario of the evolution of parameter $b_n$. In this work, we identify power-law relationships between key parameters for the chaotic transition and the iteration time. Additionally, we analyze system reversibility during the chaotic transition and demonstrate an extra transport, where parameter variation modifies the diffusion coefficient.
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