# Questions tagged [billiards]

Billiards are a class of dynamical systems in which a point particle moves uniformly in a domain $D\subset \mathbb{R}^d$ except for mirror-like reflections from the boundary. Varying $D$ leads to examples satisfying many ergodic properties. Billiards enhance visual explanations of dynamical concepts to students and the general public. There are many applications in physics and image processing. The free motion and/or reflection rule may be generalized.

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### Pocket billiards with balls in general position

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### Illuminating a just-barely irrational polygon

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### Maximal length of trajectories in billiard

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### Finding particular closed paths in geometric plane regions

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### Is there a reversible fully polynomial-time approximation scheme for polygonal billiards?

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### Why are we interested in operators that share a basis of eigenfunctions?

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### Why is the billiard problem for obtuse triangles so hard?

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### Trapping lightrays under nonstandard reflections and/or paths

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### Types of triangles admitting periodic billiard orbits

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### 6-periodic billiards trajectory in acute triangle

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### Under which conditions do ellipsoids have a focal property?

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### Can one “hear” the shape of a polygon via external reflections?

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### Infinite number of points reflecting on the circle, must some two (or more) ever meet?

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### Trapping lightrays with segment mirrors

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### A Really Simple Stochastic Dynamic Billiard

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### 3D Billiards problem inside a torus

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### A question about billiards

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### Current state of Straus's illumination problem

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### Existence of periodic orbits in rational billiards

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### Periodic billiard paths in hyperbolic triangles

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### Boundedness of partial products for a divergent trig product

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### Complexity of recognizing equivalent translation surfaces

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### How much energy will be released in the explosion when one shoots a superelastic billiard ball into a collection of still superelastic billiard balls?

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### Mathematical Billiards: Set of starting points and velocities hitting boundary at time t

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### Are periodic billiard trajectories stable on a manifold with strictly convex boundary?

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### Trapped Billiard trajectories on non-convex billiard tables

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### Reflection of light from function graph

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### Which polygons have *simple* periodic billiard paths?

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### What “real life” problems can be solved using billiards?

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### The view from inside of a mirrored tetrahedron

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### Billiard dynamics with angle of reflection a fraction of angle of incidence

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### Unfoldings of trajectories on the Veech triangle $V_4$

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### Existence of nonergodic polygonal billiard

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### Raphael Douady's thesis: Applications du théorème des tores invariants

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### Perfectly centered break of a perfectly aligned pool ball rack

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### Well-definedness of single-particle smooth billiards flow

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### A special tessellation

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### square-tiled surfaces and the Euler phi function

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### Reference for standard lemmas in polygonal billiards

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### Computing saddle connections in flat structures

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### Can every $\mathbb{Z}^2$ disk be pinball-reached?

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### Do identical orbit tiles imply identical combinatorial types?

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### Reference question: Poncelet theorem

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### Does the $n$-gonal billiards conjecture follow from the $m$-gonal conjecture when $m>n$?

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### Pinball on the infinite plane

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### Optic fibers after Joseph O'Rourke

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### Polygon illumination with perturbed reflections

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### Billiard dynamics under gravity

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### Light rays bouncing in twisted tubes

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