Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 11 min ago
PreprintCC BY 4.0arXiv

Persistence of invariant graphs for twist maps under analytic perturbations

  • Qi Li
  • Yi Liu
  • Lin Wang
Open at sourcePDFDOICite

Abstract

We construct high-frequency perturbations of an integrable exact symplectic twist map which preserve an analytic invariant graph with a prescribed rotation number. Their oscillation frequencies may be any positive integers tending to infinity. For every fixed Gevrey parameter L>0, the perturbations tend to zero in a Gevrey-α norm and diverge in a Gevrey-(α−ε) norm. The frequency class strictly contains the α-Brjuno--Rüssmann class, and their difference has cardinality 2ℵ0.

Related

  1. Quantitative Persistence and Regularity of Invariant Graphs for Dissipative Twist Maps
    Deyu Kong, Jessica Elisa Massetti, Lin Wang
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  2. On Standard perturbations of the Affine twist map
    Salvador Addas Zanata
    arXivPreprintCC BY-NC-SA 4.0Full textDynamical systemsarXiv
  3. Property (R) with its stability for analytic functional system and under compact perturbations
    Sinan Qiu, Lining Jiang, Xiaomin Wei
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices
    Pierre Bousseyroux, Marc Potters
    arXivPreprintarXiv licenceFull textMathematical physicsProbabilityarXiv
  5. On the sharpness of the C1-norm threshold for perturbations in the normally hyperbolic invariant manifold theorem---a toy model perspective
    Yujie Huang, Junhao Li, Lin Wang
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{li2026persistence,
  title = {{Persistence of invariant graphs for twist maps under analytic perturbations}},
  author = {Qi Li and Yi Liu and Lin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.05239},
  eprint = {2608.05239},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.05239},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Persistence of invariant graphs for twist maps under analytic perturbations
AU  - Qi Li
AU  - Yi Liu
AU  - Lin Wang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.05239
UR  - https://arxiv.org/abs/2608.05239
AB  - We construct high-frequency perturbations of an integrable exact symplectic twist map which preserve an analytic invariant graph with a prescribed rotation number. Their oscillation frequencies may be any positive integers tending to infinity. For every fixed Gevrey parameter L>0, the perturbations tend to zero in a Gevrey-α norm and diverge in a Gevrey-(α−ε) norm. The frequency class strictly contains the α-Brjuno--Rüssmann class, and their difference has cardinality 2^ℵ_0.
ER  -