243 research outputs found
Outer billiard outside regular polygons
We consider outer billiard outside regular convex polygons. We deal with the
case of regular polygons with sides, and we describe the
symbolic dynamics of the map and compute the complexity of the language.Comment: 53 pages, 12 figure
A characterization of quasi-rational polygons
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.Comment: 15 pages, 9 figure
Hyperbolic outer billiards : a first example
We present the first example of a hyperbolic outer billiard. More precisely
we construct a one parameter family of examples which in some sense correspond
to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit
Numerical exploration of a hexagonal string billiard
In this paper we are interested in the motion of a ball inside a billiard
table bounded by a particular smooth curve. This table belongs to a family of
billiards which can all be drawn by a common process: the so-called gardener's
string construction. The classical elliptical billiard is, of course, the
foremost member of this family. So it should come as no surprise that our
hexagonal string billiard shares many basic properties with the latter, but, on
the other hand, also exhibits some essential differences with it.
We have gathered numerical evidence against the Birkhoff-Poritsky conjecture.Comment: Preprint, 30 pages, 26 figure
Prevalence of marginally unstable periodic orbits in chaotic billiards
The dynamics of chaotic billiards is significantly influenced by coexisting
regions of regular motion. Here we investigate the prevalence of a different
fundamental structure, which is formed by marginally unstable periodic orbits
and stands apart from the regular regions. We show that these structures both
{\it exist} and {\it strongly influence} the dynamics of locally perturbed
billiards, which include a large class of widely studied systems. We
demonstrate the impact of these structures in the quantum regime using
microwave experiments in annular billiards.Comment: 6 pages, 5 figure
- …