4 papers · 1 filter
Product sets in sets of returns and positivity of symmetric ergodic averages
Vitaly Bergelson, Saúl RodrÃguez-MartÃn, Saúl Rodríguez-Martín
We study sets of (measurable) returns in countable groups , namely sets of the form arising from measure-preserving actions. Extending a result of B…
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
Vitaly Bergelson, Joel Moreira, Florian K. Richter
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectur…
New Applications of Ergodic Theory to Sets of Differences
Kabir Belgikar, Vitaly Bergelson, Gabriel Black +1
We apply the methods of ergodic theory to both simplify and significantly extend some classical results due to Stewart, Tijdeman, and Ruzsa. One of the notable features of our appr…
On preservation of normality and determinism under arithmetic operations
Vitaly Bergelson, Tomasz Downarowicz
In this paper we develop a general ergodic approach which reveals the underpinnings of the effect of arithmetic operations involving normal and deterministic numbers. This allows u…