Numerical non-integrability of Hexagonal string billiard
We consider a remarkable C-smooth billiard table introduced by Hans L. Fetter . It is obtained by the string construction from a regular hexagon for a special value of the length of the string. It…
Non-smooth convex caustics for Birkhoff billiard
This paper is devoted to the examination of the properties of the string construction for the Birkhoff billiard. Based on purely geometric considerations, string construction is suited to provide a…
Elliptic flowers: simply connected billiard tables where chaotic (non-chaotic) flows move around chaotic (non-chaotic) cores
We introduce a class of billiards with chaotic unidirectional flows (or non-chaotic unidirectional flows with ‘vortices’) which go around a chaotic or non-chaotic ‘core’, where orbits can change…
Billiard dynamics: an updated survey with the emphasis on open problems.
This is an updated and expanded version of the earlier survey article "Billiard dynamics: a survey with the emphasis on open problems," which introduced the subject matter and reported on the recent work pertaining to the problems and conjectures exposed.
SHOWING 1-10 OF 37 REFERENCES
Billiards that Share a Triangular Caustic
We consider a one-parameter family of billiard tables Tl which have as a common caustic the equilateral triangle γ. The billiard tables Tl are constructed geometrically by the string construction,…
Numerical exploration of a family of strictly convex billiards with boundary of classC2
We are interested in the possible existence of strictly convex ergodic billiards. Such billiards are searched for by means of numerical investigation. The boundary of a billiard is built with four…
Classical dynamics of a family of billiards with analytic boundaries
The classical dynamics of a billiard which is a quadratic conformal image of the unit disc is investigated. The author gives the stability analysis of major periodic orbits, present the Poincare…
Caustics for inner and outer billiards
With a plane closed convex curve,T, we associate two area preserving twist maps: the (classical) inner billiard inT and the outer billiard in the exterior ofT. The invariant circles of these twist…
In investigating dynamical billiard theory, we focus on two important examples that demonstrate a variety of behaviors and represent clear gradation in complexity. This paper mixes analytic and…
Instability of the boundary in the billiard ball problem
We consider the billiard ball problem in the interior of a plane closed convexC1 curve which is piecewiseC2. If the curvature has a discontinuity, then the boundary is unstable, i.e. no caustics…
Geometric derivations of the second constant of motion for an elliptic 'billiard' and other results
- Mathematics, Physics
The product of the focal angular momenta of an elliptic billiard is a conserved quantity, which is known as the second constant of motion. Its value can be derived both dynamically and geometrically.…
- MathematicsErgodic Theory and Dynamical Systems
Abstract Consider the billiard ball problem in an open, convex, bounded region of the plane whose boundary is C2 and has at least one point of zero curvature. Then there are trajectories which come…
Chaotic behavior in lemon-shaped billiards with elliptical and hyperbolic boundary arcs.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
Chaotic properties of a new family of lemon-shaped two-dimensional billiards, interpolating between the square and the circle, whose boundaries consist of hyperbolic, parabolic, or elliptical segments, depending on the shape parameter delta are investigated classically and quantally.