AI 中文总结
本文研究平均场耦合系统中自洽传递算子的动力学，证明在弱耦合下算子有唯一不动点且指数吸引锥内所有密度轨道。
AI 中文摘要
我们研究了与平均场耦合系统相关的自洽传递算子的动力学，其中单元动力学由具有有限多个尖点型奇点的区间映射给出。我们证明，当耦合强度足够弱时，此类算子在相应巴拿赫空间的适当锥中具有唯一不动点，并且该不动点以相应范数下的指数速率吸引锥中每个密度的轨道。
英文摘要
We study the dynamics of self-consistent transfer operators associated with mean-field coupled systems whose unit dynamics is given by an interval map with finitely many singularities of cusp type. We show that, when the coupling strength is sufficiently weak, such an operator has a unique fixed point in a suitable cone of the associated Banach space, and that this fixed point attracts the orbit of every density in the cone at an exponential rate in the corresponding norm.
CommentsTo appear in Journal of Fixed Point Theory and Applications
