Geodesic
Spectral properties of ergodic dynamical systems conjugate to their composition squares
Geoffrey R. Goodson1
1 Department of Mathematics Towson University Towson, MD 21252, U.S.A.
Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 99-118.

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Let $S$ and $T$ be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation $ST=T^2S$ are given for $T$ ergodic and also when $T^n=I$ for some $n>2$. These ideas are used to construct examples of ergodic automorphisms $S$ with oscillating maximal spectral multiplicity function. Other examples illustrating the theory are given, including Gaussian automorphisms having simple spectra and conjugate to their squares.
DOI : 10.4064/cm107-1-10
Keywords: automorphisms standard borel probability space ergodic spectral consequences equation given ergodic these ideas construct examples ergodic automorphisms oscillating maximal spectral multiplicity function other examples illustrating theory given including gaussian automorphisms having simple spectra conjugate their squares

Geoffrey R. Goodson 1

1 Department of Mathematics Towson University Towson, MD 21252, U.S.A. 
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Geoffrey R. Goodson. Spectral properties of ergodic dynamical systems
 conjugate to their composition squares. Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 99-118. doi : 10.4064/cm107-1-10. http://geodesic.mathdoc.fr/articles/10.4064/cm107-1-10/

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