Related papers: Trees and flowers on a billiard table
Lensed billiards are an extension of the notion of billiard dynamical systems obtained by adding a potential function of the form $C1_{\mathcal{A}}$, where $C$ is a real valued constant and $1_{\mathcal{A}}$ is the indicator function of an…
We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width…
We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis, first put forward by [FM]: they do…
Inspired by recent work on refraction billiards in dynamics, we introduce a notion of refraction for combinatorial billiards. This allows us to define a generalization of toric promotion that we call toric promotion with reflections and…
This survey is based on a series of talks I gave at the conference "Dynamical systems and diophantine approximation" at l'Instut Henri Poincar\'e in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for…
While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are…
Any smooth surface in R^3 may be flattened along the z-axis, and the flattened surface becomes close to a billiard table in R^2 . We show that, under some hypotheses, the geodesic flow of this surface converges locally uniformly to the…
We study the deep interplay between geometry of quadrics in d-dimensional space and the dynamics of related integrable billiard systems. Various generalizations of Poncelet theorem are reviewed. The corresponding analytic conditions of…
We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…
The winning rule of billiards is to drive the billiard ball on the table into the designated holes. We try to study the trajectory of the billiard ball, so that we can predict the direction of the ball. For rational slopes, we got cutting…
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality…
We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface $M$ in a $d$-dimensional Finsler space with possibly irreversible Finsler metric. An example of such a…
We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known that the set of points whose first n-bounces hits the same…
Polygonal billiards are an example of pseudo-chaotic dynamics, a combination of integrable evolution and sudden jumps due to conical singular points that arise from the corners of the polygons. Such pseudo-chaotic behaviour, often…
This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike…
Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat $3$-manifolds which we call translation prisms. Using ideas of Furstenberg and Veech, we connect results about weak mixing properties of…
We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be…
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…
The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the…