Convergence of polynomial ergodic averages
- 113 Downloads
We prove theL2 convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials.
Unable to display preview. Download preview PDF.
- [AGH63]L. Auslander, L. Green and G. Hahn,Flows on Homogeneous Spaces, Annals of Mathematics Studies53, Princeton University Press, 1963.Google Scholar
- [FW96]H. Furstenberg and B. Weiss,A mean ergodic theorem for 1/NΣn=1n f(T n x)g(T n 2 x), inConvergence in Ergodic Theory and Probability (V. Bergelson, P. March and J. M. Rosenblatt, eds.), Walter de Gruyter & Co, Berlin, New York, 1996, pp. 193–227.Google Scholar
- [HK02]B. Host and B. Kra,Non conventional ergodic averages and nilmanifolds, Annals of Mathematics, to appear.Google Scholar
- [L02]A. Leibman,Pointwise convergence of ergodic averages for polynomial sequences of rotations of a nilmanifold, Ergodic Theory and Dynamical Systems, to appear.Google Scholar