紧流形上的混沌：Takens定理之外的可微同步
Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
摘要：
本文证明了一类由定义在紧致流形上的动力系统的离散时间观测驱动的衰减记忆状态空间系统总是产生连续可微的同步。这一结果为混沌吸引子的表示、重构和预测提供了有力的工具。它还改善了以前的陈述在文献中的可微广义同步，其存在性是迄今为止保证了一个有限的家庭系统，并检测使用霍德尔指数为基础的标准。
英文摘要：
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result provides a powerful tool for the representation, reconstruction, and forecasting of chaotic attractors. It also improves previous statements in the literature for differentiable generalized synchronizations, whose existence was so far guaranteed for a restricted family of systems and was detected using Hölder exponent-based criteria.
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。
