Time-Changes of Heisenberg nilflows

Giovanni Forni; Adam Kanigowski

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arXiv · 1711.05543

Time-Changes of Heisenberg nilflows

Giovanni Forni·Adam Kanigowski

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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.

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BibTeX RIS

Giovanni Forni, Adam Kanigowski. 2017-11-15. Time-Changes of Heisenberg nilflows. https://arxiv.org/abs/1711.05543

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