Ergodic properties of group extensions of dynamical systems with discrete spectra

• Autorzy: Mieczysław K. Mentzen
• Języki publikacji: EN

Abstrakty

EN

Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.

Kategorie tematyczne

• 28D10: One-parameter continuous families of measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 1
• Strony: 19-31

Daty

wydano

1991

otrzymano

1990-09-07

poprawiono

1990-10-17

Twórcy

autor

Mieczysław K. Mentzen

• Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557.
• [2] H. B. Keynes and D. Newton, Ergodic measures for non-abelian compact group extensions, Compositio Math. 32 (1976), 53-70.
• [3] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. 13 (1965), 397-403.
• [4] M. Lemańczyk and M. K. Mentzen, Compact subgroups in the centralizer of natural factors determine all factors, Ergodic Theory Dynamical Systems 10 (1990), 763-776.
• [5] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136.
• [6] D. Rudolph, An example of a measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122.