Banach固定点与流方法在粗糙分析中的应用
Banach fixed point and flow approach for rough analysis
AI总结：
本文研究了粗糙微分方程中固定点论证的代数假设，证明多索引霍普夫代数不满足cocycle条件，揭示了在正则结构中进行固定点论证的不可能性。
摘要：
本文证明了执行粗糙微分方程的固定点论证所需的主要代数假设暗示了Bailleul流方法所需的代数假设。该假设要求与方程相关的粗糙路径由一个霍普夫代数给出，其余弦映射具有cocycle并具有树状基。我们证明多索引霍普夫代数不满足cocycle条件。这是对多索引粗糙路径和正则结构中多索引进行固定点论证不可能性的严格结果，这一现象在实践中也已被观察到。
英文摘要：
In this paper, we show that the main algebraic assumption required to perform a fixed point argument for rough differential equations implies the algebraic assumption for the Bailleul flow approach. This assumption requires that the rough path associated with the equation is given by a Hopf algebra whose coproduct admits a cocycle and has a tree-like basis. We show that the Hopf algebra of multi-indices does not satisfy the cocycle condition. This is a rigorous result on the impossibility, observed in practice, of performing a fixed point argument for multi-indices rough paths and multi-indices in Regularity Structures.
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。
