Abstract
We study the size of the set of ergodic directions for the directional billiard flows on the infinite band ℝ × [0,h] with periodically placed linear barriers of length 0 <λ <h. We prove that the set of ergodic directions is always uncountable. Moreover, if λ/h ∈ (0, 1) is rational, the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.
| Original language | English |
|---|---|
| Pages (from-to) | 643-663 |
| Number of pages | 21 |
| Journal | Communications in Mathematical Physics |
| Volume | 327 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 26 Mar 2014 |