Geodesic
Ergodic Dynamical Systems Conjugate to their Composition Squares
Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 2 
G. R. Goodson. Ergodic Dynamical Systems Conjugate to their Composition Squares. Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2002_71_2_a6/
@article{AMUC_2002_71_2_a6,
     author = {G. R. Goodson},
     title = {Ergodic {Dynamical} {Systems} {Conjugate} to their {Composition} {Squares}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2002},
     volume = {71},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2002_71_2_a6/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.