由受控粗糙路径驱动的粗糙微分方程生成的随机动力系统
Random dynamical systems generated by rough differential equations driven by controlled rough paths
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中文总结 AI 辅助
本文研究由受控粗糙路径驱动的粗糙微分方程，通过典范提升建立路径wise适定性，构造可微解余圈，并证明局部稳定、不稳定和中心流形的不变性。
中文摘要 AI 辅助
我们研究了由带漂移的受控粗糙路径驱动的粗糙微分方程。通过受控驱动子的典范提升，我们建立了路径wise适定性和连续性。在相容的时间平移条件下，我们为这里所考虑的方程生成的关联动力系统构造了可微解余圈。此外，假设相应的正则性、矩和谱假设，我们证明了局部稳定、不稳定和中心流形的不变性。
英文摘要
We study rough differential equations driven by controlled rough paths with drift. By means of the canonical lift of the controlled driver, we establish pathwise well-posedness and continuity. Under compatible time-shift conditions, we construct differentiable solution cocycles for the associated dynamical system generated by the equations considered here. Furthermore, assuming the corresponding regularity, moment, and spectral hypotheses, we prove the invariance of the local stable, unstable, and center manifolds.
发表机构
- School of Mathematics and Statistics, Lanzhou University（兰州大学数学与统计学院）
- Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics（甘肃省数学与统计学基础学科研究中心）
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