调和分析和偏微分方程研讨班：KAM via standard fixed points

中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：Chengyang Shao（University of Chicago）

题  目：KAM via standard fixed points

时  间：2024.01.30（星期二）15:00-16:00

地  点：思源楼S803

摘  要：In this talk, we aim to introduce a new method to solve conjugacy problems involving 'small denominators’. Traditional proofs addressing the regularity loss caused by these 'small denominators' have heavily relied on Newtonian / Nash-Moser iterations. We aim to show that the regularity loss can be compensated by composing with appropriate para-differential operators, enabling a proof using only standard fixed-point schemes. This para-differential approach can be applied to study KAM-type problems, avoiding the commonly used 'KAM iterations.' The talk is based on joint works with Thomas Alazard and will focus on technical details of the approach.