A logarithm law for non-autonomous systems rapidly converging to equilibrium and mean field coupled systems
We prove that if a non-autonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior), then the time τr(x,y) needed for a typical point x to enter for the first time in a ball B(y,r) centered at y, with small radius r, scales as the local dimension of the equilibrium measure μ at y, i.e., limr→0logτr(x,y)-logr=dμ(y). We then apply the general result to concrete systems of different kinds, showing such a logarithm law for asymptotically autonomous solenoidal maps and mean field coupled expanding maps.
Authors
- Stefano Galatolo (ORCID: https://orcid.org/0000-0003-3934-5412)
- Davide Faranda (ORCID: https://orcid.org/0000-0001-5001-5698)
Institutions
- University of Pisa (IT)
- Centre National de la Recherche Scientifique (FR)
- Université de Versailles Saint-Quentin-en-Yvelines (FR)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Université Paris-Saclay (FR)
- Laboratoire des Sciences du Climat et de l'Environnement (FR)
- CEA Paris-Saclay (FR)
Publication Details
- Journal
- Chaos An Interdisciplinary Journal of Nonlinear Science
- Published
- 2025-02-01
- DOI
- https://doi.org/10.1063/5.0221721
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Università di Pisa