Ergodic Theory and Dynamical Systems

Table of Contents - 2006 - Volume 26, Issue 03  


Strange adding machines

LOUIS BLOCK a1, JAMES KEESLING a1 and MICHAL MISIUREWICZ a2
a1 Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA (e-mail: block@math.ufl.edu, jek@math.ufl.edu)
a2 Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, IN 46202-3216, USA (e-mail: mmisiure@math.iupui.edu)

Article author query
block l   [Google Scholar] 
keesling j   [Google Scholar] 
misiurewicz m   [Google Scholar] 
 

Abstract

We show that given an adding machine of type $\alpha$, for a dense set of parameters $s$ in the interval $[\sqrt2,2]$, if $f$ is the tent map with slope $s$, then the restriction of $f$ to the closure of the orbit of the turning point is topologically conjugate to the adding machine map of type $\alpha$.

(Received January 30 2005)
(Revised November 4 2005)