Averaging theorems for slow fast systems in $\mathbb{Z}$-extensions (discrete time)
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913202496864256 |
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| author | Phalempin, Maxence |
| author_facet | Phalempin, Maxence |
| contents | We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of future development, we establish our results in a general context of perturbation by $\mathbb Z$-extension over chaotic probability preserving dynamical systems. As a by product, we prove limit theorems for non-stationary Birkhoff sums for such infinite measure preserving dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Averaging theorems for slow fast systems in $\mathbb{Z}$-extensions (discrete time) Phalempin, Maxence Dynamical Systems We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of future development, we establish our results in a general context of perturbation by $\mathbb Z$-extension over chaotic probability preserving dynamical systems. As a by product, we prove limit theorems for non-stationary Birkhoff sums for such infinite measure preserving dynamical systems. |
| title | Averaging theorems for slow fast systems in $\mathbb{Z}$-extensions (discrete time) |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.11277 |