腾讯会议ID：631 606 056

会议议程

报告人：高美娜

题目：A degenerate KAM theory for higher dimensional PDEs

摘要：In this talk, an infinite dimensional KAM theorem with multiple normal frequencies is established under qualitative non-degenerate conditions. This is an extension of the degenerate KAM theorem with simple normal frequencies by Bambusi, Berti and Magistrelli and the authors. As applications, for higher dimensional nonlinear Schrodinger equation with periodic boundary conditions, quasi-periodic solutions of small amplitude and quasi-periodic solutions around plane wave are obtained.

报告人; 丛洪滋

题目：The full dimensional tori for some Hamiltonian PDEs

摘要：In this talk, we will discuss the existence of the full dimensional tori for some Hamiltonian PDEs.

报告人：徐新冬

题目：Boundednes of solutions for quantum Harmonic oscillators forced by Liouvillean frequency

摘要：We study $1$ dimensional  quantum harmonic oscillators forced by Liouvillean frequency. It is proved that the solutions of such oscillators are bounded for positive measure  parameters with suitable restriction on the frequency vector.

报告人：王婧

题目：KAM theorem for Hamiltonian systems with Liouvillean frequency and applications

摘要：In this talk, we will consider the KAM theorem for finite dimensional Hamiltonian systems with Liouvillean frequency and its applications to harmonic oscillators and duffing-type equations with superquadratic quasiperiodic potentials. This talk is based on works jointly with Jiangong You, Xindong Xu, and Qi Zhou.

报告人：周麒

题目：Multiplicative Jensen's formula and quantitative global theory for one-frequency Schr\"odinger operators

摘要：We explore Avila's global theory for one-frequency Schrödinger operators from the point of view of Aubry duality. We establish the one-to-one correspondence between the Lyapunov exponent of the Schrödinger cocycles  and the Lyapunov exponents of its dual cocycles. We also give a new equivalent definition of subcritical, critical, supercritical regimes. Especially, we prove that the acceleration of the Schrödinger cocycle equals to the pair of zero Lyapunov exponents of its dual cocycle. Finally, we talk about its physical application.

报告人：石云峰

题目：Melnikov’s Problem Revisited

摘要：:In this talk, we revisit the Melnikov’s  persistence problem and illustrate that the Craig-Wayne-Bourgain method can be strengthened to obtain both the existence and linear stability of the invariant tori. The proof is free from the second Melnikov’s condition. This is based on a joint work with X. He, J. Shi and Y. Yuan.