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On the stability of rank-one factors for Anosov ℤk-actions

  • Danijela Damjanovic
  • Jiesong Zhang
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Abstract

We prove C1-stability of C∞ rank-one factors for a large class of higher rank Anosov ℤk-actions. If the factor is a projection of a smooth fiber bundle and the action contains an element which acts as the identity on the rank-one factor and is Anosov on every fiber, then any sufficiently C1-small C∞ perturbation of the action will also have a C∞ rank-one factor. In particular, we prove the C1-stability of the product structure for Anosov ℤ2-actions which are obtained as a (diagonal) product of two ℤ-Anosov actions.

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Cite

BibTeXRIS
BibTeX
@misc{damjanovic2026stability,
  title = {{On the stability of rank-one factors for Anosov $\mathbb Z^k$-actions}},
  author = {Danijela Damjanovic and Jiesong Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33228},
  eprint = {2610.33228},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33228},
}
RIS
TY  - UNPB
TI  - On the stability of rank-one factors for Anosov ℤ^k-actions
AU  - Danijela Damjanovic
AU  - Jiesong Zhang
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33228
UR  - https://arxiv.org/abs/2610.33228
AB  - We prove C^1-stability of C^∞ rank-one factors for a large class of higher rank Anosov ℤ^k-actions. If the factor is a projection of a smooth fiber bundle and the action contains an element which acts as the identity on the rank-one factor and is Anosov on every fiber, then any sufficiently C^1-small C^∞ perturbation of the action will also have a C^∞ rank-one factor. In particular, we prove the C^1-stability of the product structure for Anosov ℤ^2-actions which are obtained as a (diagonal) product of two ℤ-Anosov actions.
ER  -