Time-Changes of Heisenberg nilflows
Abstract
We consider the three dimensional Heisenberg nilflows. Under a full measure set Diophantine condition on the generator of the flow we construct Bufetov functionals which are asymptotic to ergodic integrals for sufficiently smooth functions, have a modular property and scale exactly under the renor- malization dynamics. We then prove analyticity of the functionals in the transverse directions to the flow. As a consequence of this analyticity property we derive that there exists a full measure set of nilflows such that generic (non-trivial) time-changes are mixing and moreover have a "stretched polynomial" decay of correlations for sufficiently smooth functions. Moreover we also prove that there exists a full Hausdorff dimension set of nilflows such that generic non-trivial time-changes have polynomial decay of correlations.
Cite
@article{arxiv.1711.05543,
title = {Time-Changes of Heisenberg nilflows},
author = {Giovanni Forni and Adam Kanigowski},
journal= {arXiv preprint arXiv:1711.05543},
year = {2017}
}