α-Equivalence

Kyewon Koh Park

Studia Mathematica (1998)

  • Volume: 130, Issue: 1, page 9-21
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Koh Park, Kyewon. "α-Equivalence." Studia Mathematica 130.1 (1998): 9-21. <http://eudml.org/doc/216544>.

@article{KohPark1998,
abstract = {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.},
author = {Koh Park, Kyewon},
journal = {Studia Mathematica},
keywords = {special flows; ceiling functions; -equivalence; orbit equivalence},
language = {eng},
number = {1},
pages = {9-21},
title = {α-Equivalence},
url = {http://eudml.org/doc/216544},
volume = {130},
year = {1998},
}

TY - JOUR
AU - Koh Park, Kyewon
TI - α-Equivalence
JO - Studia Mathematica
PY - 1998
VL - 130
IS - 1
SP - 9
EP - 21
AB - 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.
LA - eng
KW - special flows; ceiling functions; -equivalence; orbit equivalence
UR - http://eudml.org/doc/216544
ER -

References

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  1. [Am] W. Ambrose, Representation of ergodic flows, Ann. of Math. 42 (1941), 723-739 Zbl0025.26901
  2. [dJFR] A. del Junco, A. Fieldsteel and D. Rudolph, α - Equivalence: refinement of Kakutani equivalence, Ergodic Theory Dynam. Systems 14 (1994), 69-102. 
  3. [Ka] S. Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635-641. Zbl0060.27406
  4. [KR] K. Kamayer and D. Rudolph, Restricted orbit equivalence for actions of discrete amenable groups, preprint. 
  5. [ORW] D. S. Ornstein, D. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 262 (1982) Zbl0504.28019
  6. [Pa1] K. K. Park, An induced mixing flow under 1 and α, J. Korean Math. Anal. Appl. 195 ( 1995), 335-353. 
  7. [Pa2] K. K. Park, Even Kakutani equivalence via α- and β-equivalences, J. Math. Anal. Appl. 195 (1995), 335-353. 
  8. [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. 
  9. [Ru1] D. Rudolph, A two-valued step coding for ergodic flows, Math. Z. 150 (1976), 201-220. Zbl0325.28019
  10. [Ru2] D. Rudolph, A restricted orbit equivalence, Mem. Amer. Math. Soc. 323 (1985). 
  11. [Sh] P. Shields, The Theory of Bernoulli Shifts, Univ. of Chicago Press, 1973. Zbl0308.28011

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