Automorphisms with finite exact uniform rank

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

Abstrakty

EN

The notion of exact uniform rank, EUR, of an automorphism of a probability Lebesgue space is defined. It is shown that each ergodic automorphism with finite EUR is finite extension of some automorphism with rational discrete spectrum. Moreover, for automorphisms with finite EUR, the upper bounds of EUR of their factors and ergodic iterations are computed.

Kategorie tematyczne

• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991
• Tom: 100
• Numer: 1
• Strony: 13-24

Daty

wydano

1991

otrzymano

1990-03-27

poprawiono

1990-06-26

poprawiono

1990-09-18

Twórcy

autor

Mieczysław K. Mentzen

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

Bibliografia

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• [5] J. King, For mixing transformations rank $(T^k) = k · rank(T)$, Israel J. Math. 56 (1986), 102-122.
• [6] M. Lemańczyk and M. K. Mentzen, on metric properties of substitutions, Compositio Math. 65 (1988), 241-263.
• [7] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136.
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• [9] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987.
• [10] V. A. Rokhlin, On fundamental ideas in measure theory, Mat. Sb. 25 (67) (1) (1949), 107-150 (in Russian)