Related papers: Aperiodic points for outer billiards
In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubular neighborhoods of translated subtori (the so called…
The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced, and make a synthesis of those.
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…
In our paper we study periodic geodesic motion on multidimensional ellipsoids with elastic impacts along confocal quadrics. We show that the method of isoperiodic deformation is applicable.
In this note we establish the existence of a (n+1)-periodic billiard trajectory inside an n-dimensional regular simplex in the hyperbolic space, which hits the interior of every facet exactly once.
We consider polygonal billiards and we show the uniqueness of coding of non-periodic billiard trajectories in polygons whose holes have non-zero minimal diameters, generalising a theorem of Galperin, Kr\"uger and Troubetzkoy.
By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limacon billiards. The statistics of these bifurcation shows that the size of the stable intervals…
In this paper we prove that in any analytic one-parameter family of twist maps of the annulus, homotopically invariant curves filled with periodic points corresponding to a given rotation number, either exist for all values of the…
We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…
We study billiards in plane domains, with a perpendicular magnetic field and a potential. We give some results on periodic orbits, KAM tori and adiabatic invariants. We also prove the existence of bound states in a related scattering…
We investigate the semiclassical energy spectrum of quantum elliptic billiard. The nearest neighbor spacing distribution, level number variance and spectral rigidity support the notion that the elliptic billiard is a generic integrable…
A periodic trajectory on a polygonal billiard table is stable if it persists under any sufficiently small perturbation of the table. It is a standard result that a periodic trajectory on an $n$-gon gives rise in a natural way to a closed…
We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those surfaces arising from rational polygonal billiards.
We study self-intersected N-periodics in the elliptic billiard, describing new facts about their geometry (e.g., self-intersected 4-periodics have vertices concyclic with the foci). We also check if some invariants listed in "Eighty New…
We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not…
A comprehensive study of periodic trajectories of billiards within ellipsoids in $d$-dimensional Euclidean space is presented. The novelty of the approach is based on a relationship established between periodic billiard trajectories and…
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does…
Any periodic trajectory on an isosceles triangle gives rise to a periodic trajectory on a right triangle obtained by identifying the halves of the original triangle. We examine the relationship between periodic trajectories on isosceles…
A uniformly discrete Euclidean graph is a graph embedded in a Euclidean space so that there is a minimum distance between distinct vertices. If such a graph embedded in an $n$-dimensional space is preserved under $n$ linearly independent…
The long time algebraic relaxation process in spatially periodic billiards with infinite horizon is shown to display a self-similar time asymptotic form. This form is identical for a class of such billiards, but can be different in an…