Related papers: Linear stability in billiards with potential
We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder…
Dynamical billiards, or the behavior of a particle traveling in a planar region $D$ undergoing elastic collisions with the boundary, has been extensively studied and is used to model many physical phenomena such as a Boltzmann gas. Of…
We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting,…
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is…
Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincar\'e map, describing evolution from an impact to the next impact, is described. Displacement of…
A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are…
A class of Hamiltonian impact systems exhibiting smooth near integrable behavior is presented. The underlying unperturbed model investigated is an integrable, separable, 2 degrees of freedom mechanical impact system with effectively bounded…
Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\lambda = 2E/\omega^{2}$ where…
We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall. Motivated by Boltzmann's original billiard model we explore…
We investigate chaotic scattering on an attractive step potential with a quadrupolar deformation. The phase space features of the bound billiard are studied by using the notion of symmetry lines to find periodic orbits. We show that the…
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in…
We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…
We present numerical and experimental results for the development of islands of stability in atom-optics billiards with soft walls. As the walls are soften, stable regions appear near singular periodic trajectories in converging (focusing)…
We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod…
The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple…
Sufficiently differentiable oval billiards always have invariant rotational curves, but there are only two types of ovals with an invariant horizontal circle in its phase-space: the constant width ovals and some very special symmetric…
In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of non-interacting particles through a small hole due…
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional…
I announce a solution of the conjecture about the measure of periodic points for planar billiard tables. The theorem says that if $\Om\subset\R^2$ is a compact domain with piecewise $C^3$ boundary, then the set of periodic orbits for the…
In an ordinary billiard trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is…