Reparametrization of flows of zero entropy
Authors:
J. Feldman and D. Nadler
Journal:
Trans. Amer. Math. Soc. 256 (1979), 289304
MSC:
Primary 28D15
MathSciNet review:
546919
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Abstract: Let , be two ergodic nparameter flows which preserve finite probability measures on their spaces X, Y. Let T be a nullsetpreserving map: sending each orbit homeomorphically to a orbit. Then , are called homeomorphically orbitequivalent. For , there has been developed a theory of such equivalence: ``Loosely Bernoulli'' theory. A completely parallel theory exists for higher dimensions, except that it is necessary to impose a certain natural ``growth'' restriction on T, a restriction which is vacuous in the case . In this paper we carry out this program, but only for the case of zero entropy.
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Imp. Acad. Tokyo 19 (1943), 635–641. MR 0014222
(7,255f)
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B. Katok, Time change, monotone equivalence, and standard dynamical
systems, Dokl. Akad. Nauk SSSR 223 (1975),
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D. Nadler, Abramov's formula for reparametrizations of nflows (to appear).
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 [R1]
D. Rudolph, Nonequivalence of measurepreserving transformations, notes.
 [R2]
, A dye theorem for nflows, (unpublished).
 [R3]
, An integrably Lipschitz reparametrization of an nflow is isomorphic to some tempered reparametrization of the same nflow (unpublished).
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E. Satayev, An invariant of monotone equivalence which determines families of automorphisms which are monotone equivalent to a Bernoulli automorphism, Proc. Fourth Sympos. on Information Theory, Part I, MoscowLeningrad, 1976. (Russian)
 [S]
Ja.
G. Sinaĭ, A weak isomorphism of transformations with
invariant measure, Dokl. Akad. Nauk SSSR 147 (1962),
797–800 (Russian). MR 0161960
(28 #5164a)
 [W]
B. Weiss, Equivalence of measure preserving transformations, Lecture Notes, Hebrew University of Jerusalem.
 [A]
 P. Abramov, Entropy of induced transformations, Dokl. Akad. Nauk SSSR 128 (1959), 647650. (Russian) MR 0113984 (22:4815)
 [D]
 H. Dye, On groups of measurepreserving transformations. I, Amer. J. Math. 81 (1959), 119159. MR 0131516 (24:A1366)
 [F1]
 J. Feldman, New Kautomorphisms and a problem of Kakutani, Israel J. Math. 24 (1976), 1637. MR 0409763 (53:13515)
 [F2]
 , rentropy, equipartition, and Ornstein's isomorphism theorem in (to appear).
 [K]
 S. Kakutani, Induced measurepreserving transformation, Proc. Imp. Acad. Tokyo 19 (1943), 635641. MR 0014222 (7:255f)
 [Ka]
 A. Katok, Time change, monotone equivalence, and standard dynamical systems, Dokl. Akad. Nauk SSSR 273 (1975), 789792. (Russian) MR 0412383 (54:509)
 [L]
 D. Lind, Locally compact measurepreserving flows, Advances in Math. 15 (1975), 175193. MR 0382595 (52:3477)
 [N]
 D. Nadler, Abramov's formula for reparametrizations of nflows (to appear).
 [O]
 D. Ornstein, Randomness, ergodic theory, and dynamical systems, Yale Mathematical Monographs, No. 5.
 [PS]
 C. Pugh and M. Shub, Ergodic elements of ergodic actions, Compositio Math. 23 (1971), 115122. MR 0283174 (44:407)
 [R1]
 D. Rudolph, Nonequivalence of measurepreserving transformations, notes.
 [R2]
 , A dye theorem for nflows, (unpublished).
 [R3]
 , An integrably Lipschitz reparametrization of an nflow is isomorphic to some tempered reparametrization of the same nflow (unpublished).
 [Sa]
 E. Satayev, An invariant of monotone equivalence which determines families of automorphisms which are monotone equivalent to a Bernoulli automorphism, Proc. Fourth Sympos. on Information Theory, Part I, MoscowLeningrad, 1976. (Russian)
 [S]
 Ja. Sinai, A weak isomorphism of transformations with an invariant measure, Dokl. Akad. Nauk SSSR 147 (1962), 797800. (Russian) MR 0161960 (28:5164a)
 [W]
 B. Weiss, Equivalence of measure preserving transformations, Lecture Notes, Hebrew University of Jerusalem.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905469196
PII:
S 00029947(1979)05469196
Article copyright:
© Copyright 1979
American Mathematical Society
