Add to ORKGWe compute explicitly the higher order terms of the formal Taylor expansion of Mather's $\beta$-function for symplectic and outer billiards in a strictly-convex planar domain $C$. In particular, we specify the third terms of the asymptotic expansions of the distance (in the sense of the symmetric difference metric) between $C$ and its best approximating inscribed or circumscribed polygons with at most $n$ vertices. We use tools from affine differential geometry.Comment: 17 pages, 3 figure
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with t...
Let $q \ge 3$ be a period. There are at least two $(1,q)$-periodic trajectories inside any smooth st...
The goal of the first part of this note is to get an explicit formula for rotation number and Mather...
Given a planar oval, consider the maximal area of inscribed $n$-gons resp. the minimal area of circu...
Abstract. This article is concerned with the study of Mather’s β-function associated to Birkhoff bil...
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the neces...
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the neces...
Given an exact symplectic map $T$ of a cylinder with a generating function $H$ satisfying the so-cal...
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the neces...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
Weyl's expansion for the asymptotic mode density of billiards consists of the area, length, curvatur...
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with t...
Let $q \ge 3$ be a period. There are at least two $(1,q)$-periodic trajectories inside any smooth st...
The goal of the first part of this note is to get an explicit formula for rotation number and Mather...
Given a planar oval, consider the maximal area of inscribed $n$-gons resp. the minimal area of circu...
Abstract. This article is concerned with the study of Mather’s β-function associated to Birkhoff bil...
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the neces...
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the neces...
Given an exact symplectic map $T$ of a cylinder with a generating function $H$ satisfying the so-cal...
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the neces...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
This article is concerned with the study of Mather's β-function associated to Birkhoff billiards. Th...
Weyl's expansion for the asymptotic mode density of billiards consists of the area, length, curvatur...
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with t...
Let $q \ge 3$ be a period. There are at least two $(1,q)$-periodic trajectories inside any smooth st...
The goal of the first part of this note is to get an explicit formula for rotation number and Mather...