Stoker's problem for quasi-periodically forced reversible systems with multi-dimensional Liouvillean frequency

发布时间：2022-04-02 来源：赢咖3 浏览次数：

Speaker:	司建国	DateTime:	2022年4月5日（周二）下午3:00-4:00
Brief Introduction to Speaker: 司建国，山东大学教授		Place:	腾讯会议：201 189 991
Abstract: In this talk, we consider a class of quasi-periodically forced reversible systems, obtained as perturbations of a set of harmonic oscillators, and study the Stoker's problem (the existence of response solutions) of such systems in the case of Liouvillean frequency. This is based on a finite dimensional KAM (Kolmogorov-Arnold-Moser) theory for quasi-periodically forced reversible systems with multi-dimensional Liouvillean frequency . As we know, the results existing in the literature deal with two-dimensional frequency, and exploit the theory of continued fractions to control the small divisor problem. The results in this paper partially extend the analysis to higher dimensional frequency and impose a non-resonance condition weaker than the Brjuno cndition, so allowing a class of Liouvillean frequencies. The main idea in KAM theory is to perform a first normal form reduction, in which the non-resonance condition is required to solve the homological equation, and then to impose fur...