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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