Ergodic directions for billiards in a strip with periodically located obstacles

Abstract

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\mathbb{R}\times [0,h]$ with periodically placed linear barriers of length $0<\lambda <h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda /h\in (0,1)$ 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.

The article is complementary to arXiv:1109.4584

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