Skip to content
DraconiticResearch
Search Sources API
186,631 studies31 sourcesUpdated 23 min ago
PreprintarXiv licencearXiv

Bernoulli property for skew products of exponentially mixing systems over Anosov bases

  • Changguang Dong
  • Qiujie Qiao
Open at sourcePDFDOICite

Abstract

We study C1+β skew products over topologically mixing Anosov diffeomorphisms, with fiber dynamics generated by a locally free ℝk-action. For a Gibbs measure on the base and a cocycle with a nonzero average, we establish a Bernoulli criterion for ergodic invariant product measures. The fiber hypotheses apply to actions that are exponentially mixing with respect to the SRB measure, as well as volume measures that are almost exponentially mixing with a limit SRB measure. As an application, when the fibers are generated by geodesic flows or Weyl chamber actions, our results reveal a statistical phase transition determined by the drift.

Related

  1. The Bernoulli property for PSL2ℝ skew products over exponentially mixing base
    Meg Doucette
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  2. Δ*-Mixing and Products of Full-Scattering Systems
    Hui Xu
    arXivPreprintCC BY-NC-SA 4.0Full textDynamical systemsarXiv
  3. Stochastic Homogenization of Schrödinger Equations with Exponentially Mixing Sub-Gaussian Potentials
    Fanfei Meng
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsProbabilityarXiv
  4. TV between Bernoulli products, up to constants
    Gleb Smirnov
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  5. Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices
    Ziyu Neroli
    arXivPreprintCC BY 4.0Full textMathematical physicsProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{dong2026bernoulli,
  title = {{Bernoulli property for skew products of exponentially mixing systems over Anosov bases}},
  author = {Changguang Dong and Qiujie Qiao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26018},
  eprint = {2610.26018},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26018},
}
RIS
TY  - UNPB
TI  - Bernoulli property for skew products of exponentially mixing systems over Anosov bases
AU  - Changguang Dong
AU  - Qiujie Qiao
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26018
UR  - https://arxiv.org/abs/2610.26018
AB  - We study C^1+β skew products over topologically mixing Anosov diffeomorphisms, with fiber dynamics generated by a locally free ℝ^k-action. For a Gibbs measure on the base and a cocycle with a nonzero average, we establish a Bernoulli criterion for ergodic invariant product measures. The fiber hypotheses apply to actions that are exponentially mixing with respect to the SRB measure, as well as volume measures that are almost exponentially mixing with a limit SRB measure. As an application, when the fibers are generated by geodesic flows or Weyl chamber actions, our results reveal a statistical phase transition determined by the drift.
ER  -