Authors : Kra, Bryna (Author of the conference)
CIRM (Publisher )
Abstract :
The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.
MSC Codes :
37A05
- Measure-preserving transformations
37A15
- General groups of measure-preserving transformations
37A25
- Ergodicity, mixing, rates of mixing
Language : English
Available date : 14/12/16
Conference Date : 08/12/16
Subseries : Research talks
arXiv category : Dynamical Systems ; Number Theory
Mathematical Area(s) : Number Theory ; Dynamical Systems & ODE
Format : MP4 (.mp4) - HD
Video Time : 00:49:47
Targeted Audience : Researchers
Download : https://videos.cirm-math.fr/2016-12-08_Kra_part3.mp4
|
Event Title : Probabilistic aspects of multiple ergodic averages / Aspects probabilistes des moyennes ergodiques multiples Event Organizers : Chazottes, Jean-René ; Kraaikamp, Cor ; Redig, Frank Dates : 05/12/16 - 09/12/16
Event Year : 2016
Event URL : http://conferences.cirm-math.fr/1512.html
DOI : 10.24350/CIRM.V.19099203
Cite this video as:
Kra, Bryna (2016). Multiple ergodic theorems: old and new - Lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19099203
URI : http://dx.doi.org/10.24350/CIRM.V.19099203
|
Bibliography
- Host, B., & Kra, B. (2005). Nonconventional ergodic averages and nilmanifolds. Annals of Mathematics Second Series, 161(1), 397-488 - http://dx.doi.org/10.4007/annals.2005.161.397
- Host, B., & Kra, B. (2005). Convergence of polynomial ergodic averages. Israel Journal of Mathematics, 149, 1-19 - http://dx.doi.org/10.1007/BF02772534
- Leibman, A. (2005). Convergence of multiple ergodic averages along polynomials of several variables. Israel Journal of Mathematics, 146, 303-315 - http://dx.doi.org/10.1007/BF02773538
- Walsh, M.N. (2012). Norm convergence of nilpotent ergodic averages
Annals of Mathematics Second Series, 175(3), 1667-1688 - http://dx.doi.org/10.4007/annals.2012.175.3.15