Variational properties of a nonlinear elliptic equation and rigidity

经典台球的椭圆非退化性与谱刚性

Elliptic non-degeneracy and spectral rigidity of classical billiards

该研究证明椭球上经典型Liouville台球桌的台球映射在椭圆不动点处非退化，并由此推导出一个谱刚性结果。

一类带应用的椭圆拟变分-半变分不等式

A class of elliptic quasi-variational-hemivariational inequalities with applications

本文研究了自反Banach空间中包含凸势、局部Lipschitz超势和解依赖约束集的一类椭圆拟变分-半变分不等式，基于不动点定理证明了解的存在性与紧致性，并通过半渗透模型实例验证了其适用性。

Variational principle for nonhyperbolic ergodic measures: Skew products and elliptic cocycles

For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems we consider are partially hyperbolic with one-dimension central direction for which there are positive entropy ergodic measures whose central Lyapunov exponent is negative, zero, or positive. We construct ergodic measures with zero central Lyapunov exponent whose entropy is positive and arbitrarily close to the topological entropy of the set of points with central Lyapunov exponent zero. This provides a restricted variatio…

From K.A.M. Tori to Isospectral Invariants and Spectral Rigidity of Billiard Tables

This article is a part of a project investigating the relationship between the dynamics of completely integrable or close to completely integrable billiard tables, the integral geometry on them, and the spectrum of the corresponding Laplace-Beltrami operators. It is concerned with new isospectral invariants and with the spectral rigidity problem for families of Laplace-Beltrami operators with Dirichlet, Neumann or Robin boundary conditions, associated with C^1 families of billiard tables. We introduce a notion of weak isospectrality for such deformations. The main dynamical assumption on the i…