Decorrelation estimates for translated measures under diagonal flows

Autor:	Björklund, Michael, Fregoli, Reynold, Gorodnik, Alexander
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	A profound link between Homogeneous Dynamics and Diophantine Approximation is based on an observation that Diophantine properties of a real matrix $B$ are encoded by the corresponding lattice $\Lambda_B$ translated by a multi-parameter semigroup $a(t)$. We establish quantitative decorrelation estimates for measures supported on leaves $a(t)\Lambda_B$ with the error terms depending only on the minimum of the pairwise distances between the parameters. The proof involves a careful analysis of the translated measures in the products of the spaces of unimodular lattices and establishes quantitative equidistributions to measures supported on various intermediate homogeneous subspaces.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.11942 Zobrazit plný text záznamu View this record from Arxiv