Pitchfork奇点附近的离散快慢系统
Discretized Fast-Slow Systems near Pitchfork Singularities
摘要：
受规范形式的快慢常微分方程表现出干草叉奇异性，我们考虑离散时间动力系统，这是通过显式欧拉法的应用程序。通过跟踪奇点附近的轨迹，我们证明了慢流形如何延伸到奇点之外，并给出了一个过渡映射的收缩率的估计。证明依赖于适合离散设置的爆破方法，其中一个关键的技术贡献是对中央重新缩放图中的立方映射的精确估计。
英文摘要：
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking trajectories in the vicinity of the singularity we show, how the slow manifold extends beyond the singular point and give an estimate on the contraction rate of a transition mapping. The proof relies on the blow-up method suitably adapted to the discrete setting where a key technical contribution are precise estimates for a cubic map in the central rescaling chart.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
