A simple proof for a $C^\infty$ Nekhoroshev theorem

时间拟周期扰动P-陡系统的Nekhoroshev定理

Nekhoroshev Theorem for time quasiperiodic perturbations of P-Steep systems

针对时间拟周期扰动的可积哈密顿系统，在可积部分满足P-陡条件下，证明扰动大小ε的指数长时间内作用变量近似守恒。

Another proof of Burguet's existence theorem for SRB measures of $C^\infty$ surface diffeomorphisms

Recently, Burguet proved a strong form of Viana's conjecture on physical measures, in the special case of $C^\infty$ surface diffeomorphisms. We give another proof, based on our analysis of entropy and Lyapunov exponents in [BCS].

Full proof of Kwapień's theorem on representing bounded mean zero functions on $[0,1]$

In [7], Kwapień announced that every mean zero function $f\in L_\infty[0,1]$ can be written as a coboundary $f = g\circ T -g$ for some $g\in L_\infty[0,1]$ and some measure preserving transformation $T$ of $[0,1]$. Whereas the original proof in [7] holds for continuous functions, there is a serious gap in the proof for functions with discontinuities. In this article we fill in this gap and establish Kwapień's result in full generality. Our method also allows to improve the original result by showing that for any given $ε>0$ the function $g$ can be chosen to satisfy a bound $\|g\|_\infty\leq (1…

$L^{(1,\infty)}$ -Hamilton算子的唯一性与几乎每矩拉格朗日析取

Uniqueness of $L^{(1,\infty)}$-Hamiltonians and almost-every-moment Lagrangian disjunction

这篇论文是由作者撤回由于一个关键的错误证明的主要定理，定理3.10。(More特别是等式（5.18）是不正确的，因为等式的右边缺少$T^*S^1(2)$因子。）因此，$L^{(1,\infty)}$ -病例的唯一性问题仍悬而未决。