# American Institute of Mathematical Sciences

June  2006, 16(2): 343-360. doi: 10.3934/dcds.2006.16.343

## Universal skyscraper templates for infinite measure preserving transformations

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

Received  June 2005 Revised  December 2005 Published  July 2006

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.
Citation: S. Eigen, A. B. Hajian, V. S. Prasad. Universal skyscraper templates for infinite measure preserving transformations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 343-360. doi: 10.3934/dcds.2006.16.343
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