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Strange adding machines

Published online by Cambridge University Press:  24 March 2006

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

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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 $\alpha$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006 , pp. 673 - 682
Copyright
2006 Cambridge University Press