论文标题
紧凑型歧管上的混乱：超出takens定理的可区分同步
Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
论文作者
论文摘要
本文表明，由紧凑型歧管定义的动态系统的离散时间观察驱动的大量褪色的内存状态空间系统始终产生连续可区分的同步。这一总体结果为混乱吸引子的表示，重建和预测提供了强大的工具。它还改善了文献中的先前陈述，用于可区分的广义同步，到目前为止，它的存在对于受限制的系统家族可以保证，并使用基于Hölder指数的标准检测到。
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.
