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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