中科院数学与系统科学研究院
数学研究所
动力系统研究中心
学术报告会
报告人：Prof. Rafael de Llave（Georgia Institute of Technology， USA）
题 目：Quasi-periodic equilibria in quasi-periodic media: Resonance effects and depinning
时 间：06.12（星期五）, 16:30--17:30
地 点：数学院南楼N913室
摘 要：We consider problems motivated by the physics of quasi-crystals. Material deposited in them tends to minimize the energy and the problem of finding minimizing solutions has been considered in the physical and mathematical literature.
In the periodic case, Aubry and Mather developed a very powerful theory which produces equilibria which are linear with bounded fluctuations. On the other hand in the quasiperiodic case, there are examples in which there are no minimizers which differ from linear in a bounded term.
We use non-variational (KAM methods) to produce solutions which differ from linear by a bounded amount. This shows that there should be a transition between bounded fluctuations and unbounded, but it is purely understood.
Another important issue is what solutions can survive the application of an external force to the medium. In the periodic case, it has been found that there are quasi-periodic solutions but with different topology. We develop a similar theory in the quasi-periodic media case, but some new phenomena appear.
This is joint work with X. Su and Lei Zhang.
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