Geodesic
Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$
Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 889-895.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that an automorphism of a Lebesgue space may admit a partial multiple mixing on subsequences of the form $\{h_n\}$ and $\{3h_n\}$ even when its inverse does not have this property. 
@article{MZM_2003_74_6_a8,
     author = {V. V. Ryzhikov},
     title = {Partial {Multiple} {Mixing} on {Subsequences} {May} {Distinguish} between {Automorphisms} $T$ and $T^{-1}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {889--895},
     publisher = {mathdoc},
     volume = {74},
     number = {6},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a8/}
}
TY  - JOUR
AU  - V. V. Ryzhikov
TI  - Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$
JO  - Matematičeskie zametki
PY  - 2003
SP  - 889
EP  - 895
VL  - 74
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a8/
LA  - ru
ID  - MZM_2003_74_6_a8
ER  - 
%0 Journal Article
%A V. V. Ryzhikov
%T Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$
%J Matematičeskie zametki
%D 2003
%P 889-895
%V 74
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a8/
%G ru
%F MZM_2003_74_6_a8
V. V. Ryzhikov. Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$. Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 889-895. http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a8/

[1] Anosov D. V., “O vklade N. N. Bogolyubova v teoriyu dinamicheskikh sistem”, UMN, 49:5 (299) (1994), 5–20 | MR | Zbl

[2] Goodson G. R., “A survey of recent results in the spectral theory of ergodic dynamical systems”, J. Dynamical and Control Systems, 5 (1999), 173–226 | DOI | MR | Zbl

[3] Oseledets V. I., “Primer dvukh neizomorfnykh sistem s odinakovym prostym singulyarnym spektrom”, Fuknktsion. analiz i ego prilozh., 5:3 (1971), 75–79 | MR | Zbl

[4] Stepin A. M., “Spektralnye svoistva tipichnykh dinamicheskikh sistem”, Izv. AN SSSR. Ser. matem., 50 (1986), 801–834 | MR

[5] Host B., “Mixing of all orders and pairwise independent joinings of systems with singular spectrum”, Israel J. Math., 76 (1991), 289–298 | DOI | MR | Zbl

[6] Ryzhikov V. V., “Homogeneous spectrum, disjointness of convolutions, and mixing properties of dynamical systems”, Selected Russian Mathematics, 1 (1999), 13–24