Adv. Math. 388 (2021) 107853.
Peyman Eslami, Ian Melbourne and Sandro Vaienti
Abstract
Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension,
and also in higher dimensions if the map happens to be Markov.
In general, the nonconformality of multidimensional intermittent maps represents a challenge that up to now is only partially addressed.
We show how to prove sharp polynomial bounds on decay of correlations
for a class of multidimensional intermittent maps.
In addition we show that the optimal results on statistical limit laws for one-dimensional intermittent maps hold also for the maps considered here. This includes the (functional) central limit theorem and local limit theorem, Berry-Esseen estimates, large deviation estimates, convergence to
stable laws and Lévy processes, and infinite measure mixing.