Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T11:53:46.659Z Has data issue: false hasContentIssue false
  • English
  • Français

Speedups of ergodic group extensions

Published online by Cambridge University Press:  01 May 2012

ANDREY BABICHEV,
ROBERT M. BURTON and
ADAM FIELDSTEEL
ANDREY BABICHEV
Affiliation:
Wesleyan University, Middletown, CT, USA (email: ababichev@wesleyan.edu)
ROBERT M. BURTON
Affiliation:
Oregon State University, Corvallis, OR, USA (email: dr.bob.math@gmail.com)
ADAM FIELDSTEEL
Affiliation:
Wesleyan University, Middletown, CT, USA (email: afieldsteel@wesleyan.edu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We prove that for all ergodic extensions $S_{1}$ of a transformation by a locally compact second countable group $G$, and for all $G$-extensions $ S_{2} $ of an aperiodic transformation, there is a relative speedup of $ S_{1} $ that is relatively isomorphic to $S_{2}$. We apply this result to give necessary and sufficient conditions for two ergodic $n$-point or countable extensions to be related in this way.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 4 , August 2013, pp. 969 - 982
Copyright
Copyright © 2012 Cambridge University Press 

References

[AOW]Arnoux, P., Ornstein, D. S. and Weiss, B.. Cutting and stacking, interval exchanges and geometric models. Israel J. Math. 50(1–2) (1985), 160–168.CrossRefGoogle Scholar
[BF]Babichev, A. and Fieldsteel, A.. Speedups of compact group extensions, arXiv:1112.4377.Google Scholar
[B]Becker, H.. Polish group actions: dichotomies and generalized elementary embeddings. J. Amer. Math. Soc. 11(2) (1998), 397–449.CrossRefGoogle Scholar
[F]Fieldsteel, A.. Factor orbit equivalence of compact group extensions. Israel J. Math. 38(4) (1981), 289–303.Google Scholar
[G]Gerber, M.. Factor orbit equivalence of compact group extensions and classification of finite extensions of ergodic automorphisms. Israel J. Math. 57 (1987), 28–48.Google Scholar
[GS]Golodets, V. Ya. and Sinel’shchikov, S. D.. Classification and structure of cocycles of amenable ergodic equivalence relations. J. Funct. Anal. 121 (1994), 455–485.Google Scholar
[H]Herman, M.. Construction de difféomorphismes ergodiques. Unpublished manuscript, 1979.Google Scholar
[KR1]Kammeyer, J. and Rudolph, D. J.. Restricted orbit equivalence for ergodic $\mathbb {Z}^{d}$ actions, I. Ergod. Th. & Dynam. Sys. 17(5) (1997), 1083–1129.Google Scholar
[KR2]Kammeyer, J. and Rudolph, D. J.. Restricted Orbit Equivalence for Actions of Discrete Amenable Groups (Cambridge Tracts in Mathematics, 146). Cambridge University Press, Cambridge, 2002.Google Scholar
[N]Neveu, J.. Une démonstration simplifée et une extension de la formule d’Abramov sur l’entropie des transformations induites. Z. Wahrscheinlichkeitst. Verw. Geb. 13 (1969), 135–140.Google Scholar
[O]Ornstein, D. S.. Ergodic Theory, Randomness and Dynamical Systems. Yale University Press, New Haven, CT, 1970.Google Scholar
[OW]Ornstein, D. S. and Weiss, B.. Any flow is an orbit factor of any flow. Ergod. Th. & Dynam. Sys. 4 (1984), 105–116.Google Scholar
[R]Rudolph, D. J.. Restricted orbit equivalence. Mem. Amer. Math. Soc. 323 (1985), 149pp.Google Scholar
[Z]Zimmer, R.. Amenable ergodic group actions and an application to Poisson boundaries of random walks. J. Funct. Anal. 27 (1978), 350–372.Google Scholar