Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T20:28:52.130Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Abstract

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

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)