Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 39 min ago
PreprintarXiv licencearXiv

Monodromy and Isomonodromy for Linear q-Difference Systems with Coefficient Matrix Ax+B

  • Jinghong Lin
  • Qian Tang
  • Xiaomeng Xu
Open at sourcePDFDOICite

Abstract

In this paper, we construct canonical fundamental solutions for linear q-difference systems with coefficient matrix Ax+B, develop the associated isomonodromy theory, and study the differential limit as q→1. We determine the asymptotic behavior of generic isomonodromic deformations, and derive explicit formulas for their monodromy data in terms of their asymptotic leading terms. We also show that the differential limit as q→1 recovers the canonical fundamental solutions, the monodromy data, and the isomonodromic deformations of the corresponding differential systems.

Related

  1. Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step
    Vitaly Tarasov, Alexander Varchenko
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsarXiv
  2. Exact controllability and rapid stabilization of linear difference delay equations and one-dimensional hyperbolic systems
    Yacine Chitour, Sébastien Fueyo, Pierre Lissy +1
    HALPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsOptimisation & controlHALarXiv
  3. A counterexample to the Clunie--Sheil-Small coefficient-difference conjecture via quasiconformal maps
    Suman Das
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Monodromy of Tate-Linear varieties
    Livia Grammatica
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Two-step nilpotent monodromy of local systems on special varieties
    Junyan Cao, Ya Deng, Christopher Hacon +1
    HALPreprintPublisher termsFull textAlgebra & number theoryAnalysis & PDEsHAL

Cite

BibTeXRIS
BibTeX
@misc{lin2026monodromy,
  title = {{Monodromy and Isomonodromy for Linear $q$-Difference Systems with Coefficient Matrix $Ax+B$}},
  author = {Jinghong Lin and Qian Tang and Xiaomeng Xu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29520},
  eprint = {2608.29520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29520},
}
RIS
TY  - UNPB
TI  - Monodromy and Isomonodromy for Linear q-Difference Systems with Coefficient Matrix Ax+B
AU  - Jinghong Lin
AU  - Qian Tang
AU  - Xiaomeng Xu
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29520
UR  - https://arxiv.org/abs/2608.29520
AB  - In this paper, we construct canonical fundamental solutions for linear q-difference systems with coefficient matrix Ax+B, develop the associated isomonodromy theory, and study the differential limit as q→1. We determine the asymptotic behavior of generic isomonodromic deformations, and derive explicit formulas for their monodromy data in terms of their asymptotic leading terms. We also show that the differential limit as q→1 recovers the canonical fundamental solutions, the monodromy data, and the isomonodromic deformations of the corresponding differential systems.
ER  -