: 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→0log⁡τr(x,y)-log⁡r=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→0log⁡τr(x,y)-log⁡r=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.
2025
Galatolo, Stefano; Faranda, Davide
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1300067
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact