554 citations
- University of CambridgeGB52 papers
- University of OxfordGB27 papers
- University of Illinois Urbana-ChampaignUS16 papers
- Space Telescope Science InstituteUS12 papers
- University of California, IrvineUS12 papers
- California Institute of TechnologyUS11 papers
- Carnegie ObservatoriesUS11 papers
- Flatiron Institute11 papers
- Leiden UniversityNL11 papers
- Université Bourgogne Franche-ComtéFR11 papers
- University of Colorado BoulderUS11 papers
- Center for Astrophysics Harvard & SmithsonianUS10 papers
8 papers · 1 filter
An Alpern tower independent of a given partition
J. T. Campbell, J. T. Collins, R. King +2
Given a measure-preserving transformation of a probability space and a finite measurable partition of , we show how to construct an Alpern tower of…
Specifying attracting cycles for Newton maps of polynomials
James T. Campbell, Jared T. Collins
We show that for any set of n distinct points in the complex plane, there exists a polynomial p of degree at most n+1 so that the corresponding Newton map, or even the relaxed Newt…
A Hardy field extension of Szemeredi's Theorem
Nikos Frantzikinakis, Mate Wierdl
In 1975 Szemerédi proved that a set of integers of positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman showed in 1996 that the common di…
Powers of sequences and recurrence
Nikos Frantzikinakis, Emmanuel Lesigne, Mate Wierdl
We study recurrence, and multiple recurrence, properties along the -th powers of a given set of integers. We show that the property of recurrence for some given values of do…
Ergodic Theory: Recurrence
Nikos Frantzikinakis, Randall McCutcheon
We survey the impact of the Poincaré recurrence principle in ergodic theory, especially as pertains to the field of ergodic Ramsey theory.
Multiple ergodic averages for three polynomials and applications
Nikos Frantzikinakis
We find the smallest characteristic factor and a limit formula for the multiple ergodic averages associated to any family of three polynomials and polynomial families of the form $…