In this survey, we provide a concise introduction to convex billiards and describe some
recent results, obtained by the authors and collaborators, on the classification of integrable …

This book gives an extensive survey of many important topics in the theory of Hamilton–
Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly …

The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable
billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a …

The first complete proof of Arnold diffusion—one of the most important problems in
dynamical systems and mathematical physics Arnold diffusion, which concerns the …

In this article we develop an analogue of Aubry–Mather theory for a class of dissipative
systems, namely conformally symplectic systems, and prove the existence of interesting …

This paper reinterprets the Freidlin–Wentzell variational construction of the rate function in
the large deviation principle for invariant measures from the weak KAM perspective …

We consider the long-term dynamics of the vanishing stepsize subgradient method in the
case when the objective function is neither smooth nor convex. We assume that this function …

We consider the evolutionary Hamilton-Jacobi equation\begin {align*} w_t (x, t)+ H (x, Dw (x,
t), w (x, t))= 0,\quad (x, t)\in M\times [0,+\infty),\end {align*} where $ M $ is a compact …

In the present paper we prove a strong form of Arnold diffusion. Let $\mathbb {T}^ 2$ be the
two torus and $ B^ 2$ be the unit ball around the origin in $\mathbb {R}^ 2$. Fix $\rho> 0 …

On the marked length spectrum of generic strictly convex billiard tables Page 1 ON THE
MARKED LENGTH SPECTRUM OF GENERIC STRICTLY CONVEX BILLIARD TABLES GUAN …