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PreprintarXiv licencearXiv

Random dynamical systems generated by rough differential equations driven by controlled rough paths

  • Xing Gao
  • Jiaqi Liu
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Abstract

We study rough differential equations driven by controlled rough paths with drift. By means of the canonical lift of the controlled driver, we establish pathwise well-posedness and continuity. Under compatible time-shift conditions, we construct differentiable solution cocycles for the associated dynamical system generated by the equations considered here. Furthermore, assuming the corresponding regularity, moment, and spectral hypotheses, we prove the invariance of the local stable, unstable, and center manifolds.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026random,
  title = {{Random dynamical systems generated by rough differential equations driven by controlled rough paths}},
  author = {Xing Gao and Jiaqi Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24637},
  eprint = {2609.24637},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24637},
}
RIS
TY  - UNPB
TI  - Random dynamical systems generated by rough differential equations driven by controlled rough paths
AU  - Xing Gao
AU  - Jiaqi Liu
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.24637
UR  - https://arxiv.org/abs/2609.24637
AB  - We study rough differential equations driven by controlled rough paths with drift. By means of the canonical lift of the controlled driver, we establish pathwise well-posedness and continuity. Under compatible time-shift conditions, we construct differentiable solution cocycles for the associated dynamical system generated by the equations considered here. Furthermore, assuming the corresponding regularity, moment, and spectral hypotheses, we prove the invariance of the local stable, unstable, and center manifolds.
ER  -