Universal skyscraper templates for infinite measure preserving transformations

S. Eigen; A. B. Hajian; V. S. Prasad

doi:10.3934/dcds.2006.16.343

Article Contents

2006, Volume 16, Issue 2: 343-360. Doi: 10.3934/dcds.2006.16.343

This issue Previous Article Topological methods in the instability problem of Hamiltonian systems Next Article Rigorous high-dimensional shadowing using containment: The general case

Universal skyscraper templates for infinite measure preserving transformations

1.
Northeastern University, Department of Mathematics, Boston, MA 02115
2.
University of Massachusetts Lowell, Department of Mathematics, One University Avenue, Lowell, MA 01854

Received: May 31, 2005

Revised: November 30, 2005

Published: March 2006

Abstract Related Papers Cited by

Abstract

We call an ordered set $\mathbf{c} = (c(i): i \in \mathbb{N})$, of nonnegative extended real numbers $c(i)$, a universal skyscraper template if it is the distribution of first return times for every ergodic measure preserving transformation $T$ of an infinite Lebesgue measure space. If ∑ _i$ c(i)<\infty$, we give a family of examples of ergodic infinite measure preserving transformations that do not admit c as a skyscraper template.
If the distribution $\mathbf{c}$ satisfies $\gcd\{i: c(i) >0 \} = 1 $, and if either of the conditions $c(I) = \infty$ (for some integer $I$), or $i n f_i \{c(i) \} > 0$ is satisfied, then $\mathbf{c}$ is a universal skyscraper template.

Keywords:

Skyscrapers,
multitower,
infinite measure preserving automorphism,
weakly wandering,
aperiodic,
dyadic odometer.

Mathematics Subject Classification: Primary: 37A45, 28D05.

Citation:

Article Metrics

HTML views() PDF downloads(93) Cited by(0)

Universal skyscraper templates for infinite measure preserving transformations

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Universal skyscraper templates for infinite measure preserving transformations

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content