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Non-rigid disk pseudo-rotations in C1 and C1,β

  • Ziran Liu
  • Jian Wang
  • Peizheng Yu
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Abstract

We construct area-preserving irrational pseudo-rotations of the closed disk that fail to be C0-rigid. For every Brjuno rotation number we obtain C1 examples, and they may be chosen arbitrarily C1-close to the rigid rotation with the same rotation number. For 0<β<1, a weighted Brjuno condition gives C1,β examples that are arbitrarily close in the C1,β topology; this weighted range contains every rotation number with denominator-growth exponent strictly smaller than 1/β and also some numbers at the critical exponent. For a suitable Brjuno--Liouville rotation number, we also obtain an example whose derivative growth is not bounded by any polynomial.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026nonrigid,
  title = {{Non-rigid disk pseudo-rotations in $C^1$ and $C^1,β$}},
  author = {Ziran Liu and Jian Wang and Peizheng Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09986},
  eprint = {2610.09986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09986},
}
RIS
TY  - UNPB
TI  - Non-rigid disk pseudo-rotations in C^1 and C^1,β
AU  - Ziran Liu
AU  - Jian Wang
AU  - Peizheng Yu
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09986
UR  - https://arxiv.org/abs/2610.09986
AB  - We construct area-preserving irrational pseudo-rotations of the closed disk that fail to be C^0-rigid. For every Brjuno rotation number we obtain C^1 examples, and they may be chosen arbitrarily C^1-close to the rigid rotation with the same rotation number. For 0<β<1, a weighted Brjuno condition gives C^1,β examples that are arbitrarily close in the C^1,β topology; this weighted range contains every rotation number with denominator-growth exponent strictly smaller than 1/β and also some numbers at the critical exponent. For a suitable Brjuno--Liouville rotation number, we also obtain an example whose derivative growth is not bounded by any polynomial.
ER  -