α-Equivalence

• Autorzy: Kyewon Koh Park
• Języki publikacji: EN

Abstrakty

EN

We define the α - relations between discrete systems and between continuous systems. We show that it is an equivalence relation. α- Equivalence vs. even α-equivalence is analogous to Kakutani equivalence vs. even Kakutani equivalence.

Kategorie tematyczne

• 28D15: General groups of measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 1
• Strony: 9-21

Daty

wydano

1998

otrzymano

1996-07-03

poprawiono

1997-10-21

Twórcy

autor

Kyewon Koh Park

• Department of Mathematics, Ajou University, Suwon 442-749, Korea

Bibliografia

• [Am] W. Ambrose, Representation of ergodic flows, Ann. of Math. 42 (1941), 723-739
• [dJFR] A. del Junco, A. Fieldsteel and D. Rudolph, α - Equivalence: refinement of Kakutani equivalence, Ergodic Theory Dynam. Systems 14 (1994), 69-102.
• [Ka] S. Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635-641.
• [KR] K. Kamayer and D. Rudolph, Restricted orbit equivalence for actions of discrete amenable groups, preprint.
• [ORW] D. S. Ornstein, D. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 262 (1982)
• [Pa1] K. K. Park, An induced mixing flow under 1 and α, J. Korean Math. Anal. Appl. 195 ( 1995), 335-353.
• [Pa2] K. K. Park, Even Kakutani equivalence via α- and β-equivalences, J. Math. Anal. Appl. 195 (1995), 335-353.
• [Pa3] K. K. Park, A short proof of even α-equivalence, in: Algorithms, Fractals, and Dynamics (Okyama/Kyoto, 1992), Plenum, New York, 1995, 193-199.
• [Ru1] D. Rudolph, A two-valued step coding for ergodic flows, Math. Z. 150 (1976), 201-220.
• [Ru2] D. Rudolph, A restricted orbit equivalence, Mem. Amer. Math. Soc. 323 (1985).
• [Sh] P. Shields, The Theory of Bernoulli Shifts, Univ. of Chicago Press, 1973.