Sets of transfer times with small densities

2019/12/19 by Michael Björklund, Alexander Fish, Björklund, Michael +3 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1912.08999

17 pages

arxiv created 2019/12/19 · arxiv updated 2019/12/20

Abstract

We consider in this paper the set of transfer times between two measurable subsets of positive measures in an ergodic probability measure-preserving system of a countable abelian group. If the lower asymptotic density of the transfer times is small, then we prove this set must be either periodic or Sturmian. Our results can be viewed as ergodic-theoretical extensions of some classical sumset theorems in compact abelian groups due to Kneser. Our proofs are based on a correspondence principle for action sets which was developed previously by the first two authors.

Cited by

• Periodicity of point processes in abelian groups without lattices

Related

• Approximate invariance for ergodic actions of amenable groups
• Plünnecke inequalities for countable abelian groups
• Szemeredi-type theorems for subsets of locally compact abelian groups of positive upper Banach density
• The ergodic theorem for additive cocycles of ℤ d or ℝ d
• New spectral multiplicities for ergodic actions