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PreprintCC BY 4.0arXiv

Dolgopyat estimate for partially hyperbolic systems: limit theorems and exponential mixing

  • Roberto Castorrini
  • Kasun Fernando
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Abstract

We prove a Dolgopyat-type estimate for the twisted transfer operators of a class of two-dimensional partially hyperbolic endomorphisms of the torus, not necessarily skew-products. The twist satisfies a quantitative transversality condition on the cotangent dynamics of the associated three-dimensional extension which, in the skew-product case, is related to Tsujii's notions of transversality and partial captivity conditions. We use the main estimate to prove higher order expansions in the central and mixing local limit theorems for the two-dimensional base, including the case of several ergodic absolutely continuous invariant measures, and we prove exponential decay of correlations for the associated three-dimensional circle extensions, with a partially hyperbolic base.

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Cite

BibTeXRIS
BibTeX
@misc{castorrini2026dolgopyat,
  title = {{Dolgopyat estimate for partially hyperbolic systems: limit theorems and exponential mixing}},
  author = {Roberto Castorrini and Kasun Fernando},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06314},
  eprint = {2611.06314},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06314},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Dolgopyat estimate for partially hyperbolic systems: limit theorems and exponential mixing
AU  - Roberto Castorrini
AU  - Kasun Fernando
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06314
UR  - https://arxiv.org/abs/2611.06314
AB  - We prove a Dolgopyat-type estimate for the twisted transfer operators of a class of two-dimensional partially hyperbolic endomorphisms of the torus, not necessarily skew-products. The twist satisfies a quantitative transversality condition on the cotangent dynamics of the associated three-dimensional extension which, in the skew-product case, is related to Tsujii's notions of transversality and partial captivity conditions. We use the main estimate to prove higher order expansions in the central and mixing local limit theorems for the two-dimensional base, including the case of several ergodic absolutely continuous invariant measures, and we prove exponential decay of correlations for the associated three-dimensional circle extensions, with a partially hyperbolic base.
ER  -