随机亚稳态系统的平均化
Averaging for random metastable systems
AI总结：
本文研究随机扰动下具有两个不变子区间的扩张映射，证明其不变密度可由初始密度的凸组合近似，并确定第二Oseledets空间的极限，推广至多不变集情形。
摘要：
随机亚稳态现象发生在外部驱动或含噪系统拥有多个表观平衡态时。本文研究一类随机动力系统，该类系统源于对区间上一维分段光滑扩张映射的扰动，该映射具有两个不变子区间，每个子区间支撑唯一的遍历绝对连续不变测度。扰动后，这种不变性被破坏，使得轨迹能够在子区间之间随机切换。我们证明，随机扰动系统的不变密度可以通过对两个初始不变密度进行平均得到的显式凸组合来近似。此外，我们还确定了当扰动趋近于零时第二Oseledets空间（即相干结构）的极限。我们的结果应用于遍历、保测且可逆驱动系统上的随机配对帐篷映射。最后，我们给出了对具有多于两个初始不变集的系统的推广。
英文摘要：
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise smooth expanding map of the interval with two invariant subintervals, each supporting a unique ergodic absolutely continuous invariant measure. Upon perturbation, this invariance is destroyed, allowing trajectories to randomly switch between subintervals. We show that the invariant density of the randomly perturbed system may be approximated by an explicit convex combination of the two initially invariant densities, obtained by averaging. Further, we also identify the limit of the second Oseledets space, or coherent structure, as the perturbation shrinks to zero. Our results are applied to random paired tent maps over ergodic, measure-preserving, and invertible driving systems. Finally, we provide generalisations to systems admitting more than two initially invariant sets.
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。
