Billiard dynamics: a survey with the emphasis on open problems

Cites Work

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Capillary floating and the billiard ball problem
Moduli spaces of quadratic differentials
Insecure configurations in lattice translation surfaces, with applications to polygonal billiards
Growth of the number of geodesics between points and insecurity for Riemannian manifolds
Insecurity for compact surfaces of positive genus
Birkhoff billiards are insecure
Topological entropy and blocking cost for geodesics in Riemannian manifolds
Configuration spaces of planar mechanical linkages with one degree of freedom
A condition for minimal interval exchange maps to be uniquely ergodic
Principles for the design of billiards with nonvanishing Lyapunov exponents
The growth rate for the number of singular and periodic orbits for a polygonal billiard
Caustics and evolutes for convex planar domains
Ergodicity of billiard flows and quadratic differentials
Convex curves whose points are vertices of billiard triangles
Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
Periodic points of the billiard ball map in a convex domain
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Hausdorff dimension of sets of nonergodic measured foliations
Note on the periodic points of the billiard
On the \(K\)-property of some planar hyperbolic billiards
The billiard in a regular polygon
The \(K\)-property of \(N\) billiard balls. I
Statistical properties of dynamical systems with some hyperbolicity
Polygonal billiards with small obstacles
Three rods on a ring and the triangular billiard
Entropy, Lyapunov exponents, and mean free path for billiards
Convex billiards and a theorem by E. Hopf
Two applications of Jacobi fields to the billiard ball problem
Billiard dynamics: a survey with the emphasis on open problems
Billiards in rectangles with barriers
Hausdorff dimension of the set of nonergodic directions (with an Appendix by M. Boshernitzan)
Moduli spaces of Abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants
Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung).
Billiards on rational-angled triangles
Affine mappings of translation surfaces: Geometry and arithmetic
Hard ball systems and the Lorentz gas
Billiards in polygons: Survey of recent results.
Billiards in Finsler and Minkowski geometries
Decay of correlations and dispersing billiards.
An estimate from above of the number of periodic orbits for semi- dispersed billiards
The geometry and arithmetic of translation surfaces with applications to polygonal billiards
Instability of the boundary in the billiard ball problem
Caustics for inner and outer billiards
Hyperbolic billiards on surfaces of constant curvature
Floating bodies subject to capillary attractions
Billiards in nearly isosceles triangles
A dense \(G\)-delta set of Riemannian metrics without the finite blocking property
Sub-Riemannian geometry and periodic orbits in classical billiards
Connecting geodesics and security of configurations in compact locally symmetric spaces
Blocking of billiard orbits and security for polygons and flat surfaces
Concerning the transitive properties of geodesics on a rational polyhedron.
The billiard ball problem on a table with a convex boundary - An illustrative dynamical problem. I. The invariant integral
On Periodic Billiard Trajectories in Obtuse Triangles
Asymptotic formulas on flat surfaces
Glancing billiards
Growth rates for geometric complexities and counting functions in polygonal billiards
Obtuse Triangular Billiards I: Near the (2, 3, 6) Triangle
The growth rate of trajectories of a quadratic differential
Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories
Billiards on almost integrable polyhedral surfaces
Invariant families of cones and Lyapunov exponents
Measure theoretic entropy of the system of hard spheres
On the number of periodic reflecting rays in generic domains
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems
Topological entropy of polygon exchange transformations and polygonal billiards
Two Applications of Calculus to Triangular Billiards
Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity
Convex and Discrete Geometry
Geometry Revealed
Billiards in polygons
Dynamical systems
Geodätische Linien auf Polyederflächen.
Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
On triangular billiards

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