Abstract
In this paper an example is constructed of a flow on the torus x=αF(x, y), y=F(x, y), x, y mod 1, with continuous F>0 and irrationalα which has a mixed spectrum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J. von Neumann, “Zür Operatormethode in der klassischen Mechanik,” Ann. of Math.,33, No. 3, 587–642 (1932).
D. V. Anosov, “On the additive functional homological equation connected with the ergodic rotation of the circle,” Izv. Akad. Nauk SSSR, Ser. Matem.,36, No. 6, 1259–1274 (1973).
V. A. Rokhlin, “Selected questions in the metric theory of dynamical systems,” Usp. Matem. Nauk,4, No. 2, 57–128 (1949).
A. B. Katok and A. M. Stepin, “Approximations in ergodic theory,” Usp. Matem. Nauk,22, No. 5, 81–106 (1967).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 235–240, February, 1974.
The author is grateful to D. V. Anosov under whose supervision this result was obtained and to A. B. Katok for his attention to the work.
Rights and permissions
About this article
Cite this article
Krygin, A.B. An example of a continuous flow on the torus with mixed spectrum. Mathematical Notes of the Academy of Sciences of the USSR 15, 133–136 (1974). https://doi.org/10.1007/BF02102393
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02102393