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On the rank of von Neumann special flows

Published online by Cambridge University Press:  14 March 2017

ADAM KANIGOWSKI  and
ANTON V. SOLOMKO
ADAM KANIGOWSKI
Affiliation:
Department of Mathematics, Pennsylvania State University, McAllister Building, 54 McAllister St, PA 16801, USA email [email protected]
ANTON V. SOLOMKO
Affiliation:
University of Bristol, School of Mathematics, Howard House, Queens Avenue, Bristol BS8 1SN, UK email [email protected]
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Abstract

We prove that special flows over an ergodic rotation of the circle under a $C^{1}$ roof function with one discontinuity do not have local rank one. In particular, any such flow has infinite rank.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 6 , September 2018 , pp. 2245 - 2256
Copyright
© Cambridge University Press, 2017 

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