ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXI, 2(2002)
p. 201
Ergodic Dynamical Systems Conjugate to their Composition Squares
G. R. Goodson
Abstract.
We investigate the
question of when an ergodic automorphism $T$ is conjugate to
its composition square $T^2$, i.e., when does there exist an
automorphism $S$ with the property that $ST=T^2S$. This is a
non--generic property of automorphisms which seems to
be quite exceptional. The situation for ergodic automorphisms
having discrete spectrum and automorphisms having
the weak closure property is investigated.
AMS subject classification:
37A05
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