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Pré-Publication, Document De Travail Année : 2024

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

Résumé

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.
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Dates et versions

hal-04549099 , version 1 (17-04-2024)

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