Nonabelian Rauzy-Veech Renormalization
Dynamical Systems
2020-01-03 v1
Abstract
For any Lie group G a renormalization map R on the space of simple G-extensions of Interval Exchange Transformations is constructed. R is applied to prove weak mixing and cohomological non-equivalence of typical G-extensions over IETs, when G is a compact connected Lie group. This extends a result of Avila and Forni for U(1) to any compact connected Lie group. This is a first result on ergodic theory of nonabelian extensions over IETs.
Cite
@article{arxiv.2001.00110,
title = {Nonabelian Rauzy-Veech Renormalization},
author = {Dmitri Scheglov},
journal= {arXiv preprint arXiv:2001.00110},
year = {2020}
}
Comments
23 pages. arXiv admin note: substantial text overlap with arXiv:1910.03015