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The Bernoulli property for PSL2ℝ skew products over exponentially mixing base

  • Meg Doucette
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Abstract

We study the Bernoulli property for skew products of the form f(x,y)=(g(x),A(x)y) on M× PSL2(ℝ)/Γ, where g is a smooth, measure-preserving, exponentially mixing diffeomorphism, Γ<PSL2(ℝ) is a cocompact lattice, and A: M→ PSL2(ℝ) is a C1+α cocycle. We prove that if A has a nonzero Lyapunov exponent, then f is Bernoulli. The proof does not require that f be exponentially mixing. This provides a new method for establishing the Bernoulli property, which applies to a large class of skew products.

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Cite

BibTeXRIS
BibTeX
@misc{doucette2026bernoulli,
  title = {{The Bernoulli property for $PSL_2\mathbbR$ skew products over exponentially mixing base}},
  author = {Meg Doucette},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08017},
  eprint = {2609.08017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08017},
}
RIS
TY  - UNPB
TI  - The Bernoulli property for PSL_2ℝ skew products over exponentially mixing base
AU  - Meg Doucette
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.08017
UR  - https://arxiv.org/abs/2609.08017
AB  - We study the Bernoulli property for skew products of the form f(x,y)=(g(x),A(x)y) on M× PSL_2(ℝ)/Γ, where g is a smooth, measure-preserving, exponentially mixing diffeomorphism, Γ<PSL_2(ℝ) is a cocompact lattice, and A: M→ PSL_2(ℝ) is a C^1+α cocycle. We prove that if A has a nonzero Lyapunov exponent, then f is Bernoulli. The proof does not require that f be exponentially mixing. This provides a new method for establishing the Bernoulli property, which applies to a large class of skew products.
ER  -