Ergodic Directions for Billiards in a Strip with Periodically Located Obstacles

Krzysztof Fraczek*, Corinna Ulcigrai

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)643-663
Number of pages21
JournalCommunications in Mathematical Physics
Volume327
Issue number2
DOIs
Publication statusPublished - 26 Mar 2014

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