All Questions
8 questions
2
votes
0
answers
109
views
Proving light escapes mirrors via ergodic theory of billiards
There's a longstanding open problem concerning whether or not it's possible to trap all the light from a point source using a finite collection of circles/lines whose sides are mirrors. This seems ...
- 509
5
votes
2
answers
277
views
Examples of different levels of the ergodic hierachy (specifically: weakly mixing & merely ergodic)
I am interested in generalizing some aspects of the ergodic hierarchy (of classical dynamical systems) to quantum theory. However, while I understand the definitions of the different levels of the ...
- 649
5
votes
0
answers
166
views
Pocket billiards with balls in general position
There were at least two earlier MO questions about ideal pocket billiards.
(Ideal: frictionless, perfectly elastic collisions.)
Perfectly centered break of a perfectly aligned pool ball rack.
Does ...
- 151k
18
votes
0
answers
480
views
Trapping lightrays with segment mirrors
Q. Is it possible to trap all the light from one point source by a finite collection of two-sided disjoint segment mirrors?
I posed this question in several forums before (e.g., here
and in an ...
- 151k
3
votes
2
answers
194
views
A Really Simple Stochastic Dynamic Billiard
Consider the following stochastic dynamical system.
Fix $a > 0$, $b > 0$, $c>0$ and $v > 0$, and let $\mathbf{r}(t)=(x(t),y(t),z(t))$ be the position at time $t$ of a point which moves ...
- 640
10
votes
1
answer
324
views
A question about billiards
This is a question in a rather well investigated subject of which I know very little and I have a hard time "translating" the general results available. Let me also say that I got interested in this ...
- 34.7k
24
votes
2
answers
1k
views
Billiard dynamics for multiple balls
I am interested to learn to what extent results on billiards
in polygons have been extended to multiple balls.
Assume the balls have equal radii and the same mass,
the same initial speed, and all
...
- 151k
33
votes
4
answers
3k
views
Does there exist a shot in ideal pocket billiards?
Assume you have one shot with the cue ball in pocket billiards (a.k.a. pool), with
the game idealized in that no spin is placed on the cue ball in
the initial shot, all collisions between billiard ...
- 151k