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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2408.03009 |
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- This paper studies the asymptotic behaviour of the solution of a differential equation perturbed by a fast flow preserving an infinite measure. This question is related with limit theorems for non-stationary Birkhoff integrals. We distinguish two settings with different behaviour: the integrable setting (no averaging phenomenon) and the case of an additive "centered" perturbation term (averaging phenomenon). The paper is motivated by the case where the perturbation comes from the Z-periodic Lorentz gas flow or from the geodesic flow over a Z-cover of a negatively curved compact surface. We establish limit theorems in more general contexts.