N. Frantzikinakis

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math.DS2005

Sets of k-recurrence but not (k+1)-recurrence

N. Frantzikinakis, E. Lesigne, M. Wierdl

For every $k \in N$ , we produce a set of integers which is $k$ -recurrent but not $(k + 1)$ -recurrent. This extends a result of Furstenberg who produced a 1-recurrent set whic…

math.DS2004

Ergodic Averages for Independent Polynomials and Applications

Nikos Frantzikinakis, Bryna Kra

Szemerédi's Theorem states that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman generalized this, showing tha…

math.DS2004

Convergence of multiple ergodic averages for some commuting transformations

Nikos Frantzikinakis, Bryna Kra

We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$ , assuming that each map $T_{i}$ and each pair $T_{i} T_{j}^{- 1}$ …

math.DS2004

Polynomial Averages Converge to the Product of Integrals

Nikos Frantzikinakis, Bryna Kra

We answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials o…

math.DS2004

The Structure of Strongly Stationary Systems

Nikos Frantzikinakis

Motivated by a problem in ergodic Ramsey theory, Furstenberg and Katznelson introduced the notion of strong stationarity, showing that certain recurrence properties hold for arbitr…