Effective equidistribution for some unipotent flows in $PSL(2, \mathbb{R})^k$ mod cocompact, irreducible lattice

James Tanis

doi:10.3934/dcds.2018042

Effective equidistribution for some unipotent flows in $PSL(2, \mathbb{R})^k$ mod cocompact, irreducible lattice

Dynamical Systems 2018-08-03 v4

Authors: James Tanis

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Abstract

Let $d \geq 2$ , and let $\Gamma \subset PSL(2, \mathbb{R})^d$ be an irreducible, cocompact lattice. We prove a sharp estimate up to a logarithmic factor on the rate of equidistribution of coordinate horocycle flows on $\Gamma \backslash PSL(2, \mathbb{R})^d$ .

Keywords

effective equidistribution unipotent flows horocycle flows cocompact lattice irreducible lattice PSL(2, R)

Cite

@article{arxiv.1412.5353,
  title  = {Effective equidistribution for some unipotent flows in $PSL(2, \mathbb{R})^k$ mod cocompact, irreducible lattice},
  author = {James Tanis},
  journal= {arXiv preprint arXiv:1412.5353},
  year   = {2018}
}

Comments

12 pages. This is part of an expanded paper titled "Exponential multiple mixing for some partially hyperbolic flows on products of $PSL(2,\mathbb{R}$)," published in DCDS - A, 2018, 38 (3) : 989-1006

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