Ergodic measure preserving transformations with arbitrary finite spectral multiplicities
Tóm tắt
Từ khóa
Tài liệu tham khảo
Baxter, J.R.: A class of ergodic transformations having simple spectrum. Proc. Amer. Math. Soc.27, 275–279 (1971)
Chacon, R.V.: Approximation of transformations with continous spectrum. Pacific J. Math.2, 293–302 (1969)
Chacon, R.V.: Approximation and spectral multiplicity. Lecture Notes in Math. Vol. 160, pp. 18–22. Berlin-Heidelberg-New York: Springer 1970
Girsanov, I.V.: Spectra of dynamical systems generated by stationary Gaussian processes, (in Russian) Dokl. Akad. Nauk SSSR119, 851–853 (1958)
Halmos, P.R., von Neumann, J.: Operator methods in classical mechanics II. Ann. Math.43, 332–350 (1942)
Halmos, P.R.: Lectures on ergodic theory. The Math. Society of Japan, Tokyo 1956
Del Junco, A.: A transformation with simple spectrum which is not rank one. Can J. Math.29, 655–663 (1977)
Katok, A.B., Stepin, A.M.: Approximation of ergodic dynamic systems by periodic transformations. Dokl. Akad. Nauk SSSR171, 1268–1271 (1966); Soviet Math. Dokl.7, 1638–1641 (1966)
Oseledec, V.I.: The spectrum of ergodic automorphisms. Dokl. Akad. Nauk SSSR168, 776–779 (1966)
Rohlin, V.A.: Entropy of a metric automorphism (in Russian). Dokl. Akad. Nauk. SSSR124, 980–983 (1959)
Rohlin, V.A.: New progress in the theory of transformations with invariant measure. Uspekhi Mat. Nauk15, 2–36 (1960); Russian Math. Surveys15, 1–22 (1960)
Rohlin, V.A.: Lectures on the entropy theory of measure preserving transformations. Uspekhi Mat. Nauk22, (1967; Russian Math. Surveys22, (1967)
Schwartzbauer, T.: A general method for approximating measure preserving transformations. Proc. Amer. Math. Soc.24, 643–648 (1970)
Veršik, A.M.: On the theory of normal dynamic systems. Dokl. Akad. Nauk SSSR114, 9–12 (1962); Soviet Math. Dokl.3, 625–628 (1962)
Veršik, A.M.: Spectral and metric isomorphism of some normal dynamical systems. Dokl. Akad. Nauk SSSR114, 255–257 (1962); Soviet Math. Dokl.3, 693–696 (1962)
Yuzvinskii, S.A.: Metric automorphisms with a simple spectrum. Dokl. Akad. Nauk SSSR172, 1036–1038 (1967); Soviet Math. Dokl.8, 243–245 (1967)