Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
D. V. Anosov, “On the contribution of N. N. Bogolyubov to the theory of dynamical systems, ” Uspekhi Mat. Nauk [Russian Math. Surveys], 49 (1994), no. 5(299), 5–20.
G. R. Goodson, “A survey of recent results in the spectral theory of ergodic dynamical systems, ” J. Dynamical and Control Systems, 5 (1999), 173–226.
V. I. Oseledets, “An example of two nonisomorphic systems with the same simple singular spectrum, ” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 5 (1971), no. 3, 75–79.
A. M. Stepin, “The spectral properties of typical dynamical systems, ” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 50 (1986), 801–834.
B. Host, “Mixing of all orders and pairwise independent joinings of systems with singular spectrum, ” Israel J. Math., 76 (1991), 289–298.
V. V. Ryzhikov, “Homogeneous spectrum, disjointness of convolutions, and mixing properties of dynamical systems, ” Selected Russian Mathematics, 1 (1999), 13–24.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ryzhikov, V.V. Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms T and T -1 . Mathematical Notes 74, 841–847 (2003). https://doi.org/10.1023/B:MATN.0000009020.82284.54
Issue Date:
DOI: https://doi.org/10.1023/B:MATN.0000009020.82284.54