中科院数学与系统科学研究院
数学研究所
学术报告会
报告人： 苏喜锋 博士 （北京师范大学数学科学学院）
题 目：The Aubry-Mather model in the continuous limit and some related topics
时 间：11.19 (星期四) , 16:00-17:00
地 点：数学院南楼N913室
Abstract :This talk will introduce some models in the classical mechanics (especially solid state physics) and quantum mechanics associated with crystals and quasi-crystals. The models in solid state physics I will mention are the generalized Frenkel-Kontorova models on the crystals and quasi-crystals and the models in quantum mechanics will be related to the spectrum of the Schodinger operators given by the crystals and quasi-crystals (especially the Fibonacci quasi-crystals).
After surveying on these models, I will concentrate on the Aubry-Mather models and talk about the corresponding discrete weak KAM thoery. The existence of the discrete weak KAM solutions are related to the additive eigenvalue problem in ergodic optimization. I will show that the discrete weak KAM solutions converge to the weak KAM solutions for the autonomous Tonelli case as the time step goes to zero.
This is a joint work with P. Thieullen.
