A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems

Stefano Galatolo (1) , Davide Faranda (2, 3, 4, 5)

1 University of Pisa - Università di Pisa
2 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)
3 London Mathematical Laboratory
4 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
5 ESTIMR - Extrèmes : Statistiques, Impacts et Régionalisation

We prove that if a nonautonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior) then the time τ_r(x,y) needed for a typical point x to enter for the first time in a ball B(y,r) centered in y, with small radius r scales as the local dimension of the equilibrium measure μ at y, i.e. lim(r→0) log [τ_r(x,y)]/ [-log(r)] We then apply the general result to concrete systems of different kind, showing such a logarithm law for asymptotically authonomous solenoidal maps and mean field coupled expanding maps.

Mots clés: non autonomous dynamics Logarithm Law hitting time local dimension. MSC(2020):37C60; 37C30; 37N10; non autonomous dynamics; Logarithm Law; hitting time; local dimension. MSC(2020):37C60

Domaines: Systèmes dynamiques [math.DS]

Stefano Galatolo, Davide Faranda. A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems. 2024. ⟨hal-04549099⟩