论文信息 - Convergence of multiple ergodic averages for some commuting transformations

Convergence of multiple ergodic averages for some commuting transformations

We prove the L2-convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, \dots, T_{l}$, assuming that each map Ti and each pair TiTj-1 is ergodic for $i\neq j$. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.

Nikos Frantzikinakis | Bryna Kra | Bryna Kra | N. Frantzikinakis

[1] Bryna Kra,et al. Nonconventional ergodic averages and nilmanifolds , 2005 .

[2] J. Conze,et al. Théorèmes ergodiques pour des mesures diagonales , 1984 .

[3] H. Furstenberg,et al. An ergodic Szemerédi theorem for commuting transformations , 1978 .

[4] Equations fonctionnelles, couplages de produits gauches et théorèmes ergodiques pour mesures diagonales , 1993 .

[5] H. Furstenberg. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions , 1977 .

[6] V. Bergelson. Weakly mixing PET , 1987, Ergodic Theory and Dynamical Systems.

[7] T. Ziegler. A non-conventional ergodic theorem for a nilsystem , 2002, Ergodic Theory and Dynamical Systems.

[8] A. Leibman. Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold , 2004, Ergodic Theory and Dynamical Systems.