Invariant measures for general induced maps and towers

Arno Berger; Roland Zweimüller

doi:10.3934/dcds.2013.33.3885

Article Contents

2013, Volume 33, Issue 9: 3885-3901. Doi: 10.3934/dcds.2013.33.3885

This issue Previous Article On the non-homogeneous boundary value problem for Schrödinger equations Next Article Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

Invariant measures for general induced maps and towers

Arno Berger^1, and
Roland Zweimüller^2,

1.
Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
2.
Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090 Wien

Received: July 31, 2012

Revised: January 31, 2013

Published: August 2013

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Abstract

Absolutely continuous invariant measures (acims) for general induced transformations are shown to be related, in a natural way, to popular tower constructions regardless of any particulars of the latter. When combined with (an appropriate generalization of) the known integrability criterion for the existence of such acims, this leads to necessary and sufficient conditions under which acims can be lifted to, or projected from, nonsingular extensions.

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Mathematics Subject Classification: Primary: 28D05, 37A40, 37C40.

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