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Topological weak-mixing of interval exchange maps

Published online by Cambridge University Press:  12 April 2001

A. NOGUEIRA and
D. RUDOLPH
A. NOGUEIRA
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970, Rio de Janeiro, Brazil
D. RUDOLPH
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA
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Abstract

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An interval map with only one discontinuity is isomorphicto a rotation of the circle, and has continuouseigenfunctions. What we show here is that for almost every choiceof lengths of the intervals, this is the only way an irreducible intervalexchangecan have a somewhere continuous eigenfunction. We show slightly more,considering certain towers over the interval exchange, showingthat outside of a set of choices for interval lengths of measure zerothese have asomewhere continuous eigenfunction only if they are isomorphic to either arotation,or a tower of constant height over an interval exchange.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 5 , October 1997, pp. 1183 - 1209
Copyright
1997 Cambridge University Press