Mixing constructions with infinite invariant measure and spectral multiplicities
Dynamical Systems
2010-01-19 v2
Abstract
We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.
Keywords
Cite
@article{arxiv.0908.1643,
title = {Mixing constructions with infinite invariant measure and spectral multiplicities},
author = {Alexandre I. Danilenko and Valery V. Ryzhikov},
journal= {arXiv preprint arXiv:0908.1643},
year = {2010}
}