Flat surfaces, Bratteli diagrams, and unique ergodicity à la Masur
arXiv:1604.03572 · doi:10.1007/s11856-018-1636-x
Abstract
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of finite area. A criterion of unique ergodicity similar to that of Masur's for flat surface holds: if there is a subsequence of the renormalizing dynamical system which has a good accumulation point, the translation flow or Bratteli-Vershik transformation is uniquely ergodic. Related questions are explored.
20 pages, version accepted for publication
References in corpus (6)
- On the Ergodicity of Flat Surfaces of Finite Area
- Ergodicity for Infinite Periodic Translation Surfaces
- Flat surface models of ergodic systems
- Ergodic infinite group extensions of geodesic flows on translation surfaces
- Immersions and the space of all translation structures
- Indiscriminate covers of infinite translation surfaces are innocent, not devious