Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A universal divergence rate for symmetric Birkhoff Sums in infinite ergodic theory


Author: Zemer Kosloff
Journal: Trans. Amer. Math. Soc. 369 (2017), 6373-6388
MSC (2010): Primary 37A17, 37A30, 37A40; Secondary 37D40
DOI: https://doi.org/10.1090/tran/6867
Published electronically: March 30, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that there exists a universal gap in the failure of the ergodic theorem for symmetric Birkhoff sums in infinite ergodic theory.


References [Enhancements On Off] (What's this?)

  • [Aar1] Jon Aaronson, An introduction to infinite ergodic theory, Mathematical Surveys and Monographs, vol. 50, American Mathematical Society, Providence, RI, 1997. MR 1450400
  • [Aar2] Jon Aaronson, On the ergodic theory of non-integrable functions and infinite measure spaces, Israel J. Math. 27 (1977), no. 2, 163-173. MR 0444899
  • [AKW] J. Aaronson, Z. Kosloff, and B. Weiss, Symmetric Birkhoff sums in infinite ergodic theory, preprint, http://arxiv.org/abs/1307.7490.
  • [Bu] Marc Burger, Horocycle flow on geometrically finite surfaces, Duke Math. J. 61 (1990), no. 3, 779-803. MR 1084459, https://doi.org/10.1215/S0012-7094-90-06129-0
  • [MS] François Maucourant and Barbara Schapira, Distribution of orbits in $ \mathbb{R}^2$ of a finitely generated group of $ {\rm SL}(2,\mathbb{R})$, Amer. J. Math. 136 (2014), no. 6, 1497-1542. MR 3282979, https://doi.org/10.1353/ajm.2014.0045
  • [Ro] Thomas Roblin, Ergodicité et équidistribution en courbure négative, Mém. Soc. Math. Fr. (N.S.) 95 (2003), vi+96 (French, with English and French summaries). MR 2057305

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 37A17, 37A30, 37A40, 37D40

Retrieve articles in all journals with MSC (2010): 37A17, 37A30, 37A40, 37D40


Additional Information

Zemer Kosloff
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV47AL, United Kingdom
Email: z.kosloff@warwick.ac.uk

DOI: https://doi.org/10.1090/tran/6867
Received by editor(s): January 5, 2015
Received by editor(s) in revised form: May 4, 2015, and September 25, 2015
Published electronically: March 30, 2017
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society