KAM via standard fixed point theorems
科研大讨论系列报告
报告题目(Title)：KAM via standard fixed point theorems
报告人(Speaker)：邵城阳（芝加哥大学）
地点(Place)：后主楼1124
时间(Time)：2024年1月12日 下午3:30-4:30
邀请人(Inviter)：黎雄
报告摘要
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.
