相关论文: Computational study of the dynamics of an asymmetr…
We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric,…
We consider two and three-dimensional quantum billiards with discrete symmetries. We derive the first terms of the Weyl expansion for the level density projected onto the irreducible representations of the symmetry group. As an illustration…
A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary…
We study the problem of arithmetic billiards from a new perspective. We first raise a similar problem about reflecting lights inside grids. For the solution to this problem, we will give three proofs. Next, we consider a similar problem in…
Asymmetric lemon billiards was introduced in [CMZZ], where the billiard table $Q(r,b,R)$ is the intersection of two round disks with radii $r\le R$, respectively, and $b$ measures the distance between the two centers. It is conjectured…
Belinski, Khalatnikov and Lifshitz (BKL) pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a space-like singularity. We show how the use of a…
This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized…
We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincar\'e map and find…
The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…
We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature…
Astute variations in the geometry of mathematical billiard tables have been and continue to be a source of understanding their wide range of dynamical behaviors, from regular to chaotic. Viewing standard specular billiards in the broader…
We study a generalized three-dimensional stadium billiard and present strong numerical evidence that this system is completely chaotic. In this convex billiard chaos is generated by the defocusing mechanism. The construction of this…
A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric…
Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off a boundary curve. The state of the system is given by two numbers: one describing the location along the curve where the bounce occurs, and…
We introduce the concepts of rotation numbers and rotation vectors for billiard maps. Our approach is based on the birkhoff ergodic theorem. We anticipate that it will be useful, in particular, for the purpose of establishing the…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff…
A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or…