: 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.
A logarithm law for non-autonomous systems rapidly converging to equilibrium and mean field coupled systems
Stefano Galatolo;Davide Faranda
2025-01-01
Abstract
: 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.File in questo prodotto:
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