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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.17963 |
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| _version_ | 1866908843050532864 |
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| author | Liu, Xinyu Li, Yong |
| author_facet | Liu, Xinyu Li, Yong |
| contents | This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we obtain, for any observable $G$, an explicit upper bound on the deviation of the ensemble average $\langle G\rangle_t$ from its angular average $\langle \left\langle G \right\rangle_θ\rangle_{0}$ over exponentially long time scales. The bound separates contributions from the resonant neighborhood via a probability-mass term, and from the nonresonant region via a traceable $1/t$ mixing constant $C_G$, a high-frequency Fourier tail, and an explicit normal-form remainder error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17963 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Statistical Ensemble Deviation Estimates for Nearly Integrable Hamiltonian Systems Liu, Xinyu Li, Yong Dynamical Systems This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we obtain, for any observable $G$, an explicit upper bound on the deviation of the ensemble average $\langle G\rangle_t$ from its angular average $\langle \left\langle G \right\rangle_θ\rangle_{0}$ over exponentially long time scales. The bound separates contributions from the resonant neighborhood via a probability-mass term, and from the nonresonant region via a traceable $1/t$ mixing constant $C_G$, a high-frequency Fourier tail, and an explicit normal-form remainder error. |
| title | Statistical Ensemble Deviation Estimates for Nearly Integrable Hamiltonian Systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2602.17963 |