Equidistribution in the dual group of the $S$-adic integers

Title:

Equidistribution in the dual group of the $S$-adic integers

Creator:

Urban, Roman

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:758277f4-1b86-4134-8714-a009785feb46
uuid:758277f4-1b86-4134-8714-a009785feb46

Subject:

uniform distribution modulo $1$, equidistribution in probability, algebraic number fields, $S$-adele ring, $S$-integer dynamical system, algebraic dynamics, topological dynamics, and $a$-adic solenoid

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $X$ be the quotient group of the $S$-adele ring of an algebraic number field by the discrete group of $S$-integers. Given a probability measure $\mu $ on $X^d$ and an endomorphism $T$ of $X^d$, we consider the relation between uniform distribution of the sequence $T^n\bold {x}$ for $\mu $-almost all $\bold {x}\in X^d$ and the behavior of $\mu $ relative to the translations by some rational subgroups of $X^d$. The main result of this note is an extension of the corresponding result for the $d$-dimensional torus $\mathbb T^d$ due to B. Host.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

911-931

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:4

Harvested from:

CDK

Metadata only:

false