Maximal S -expansions are Bernoulli shifts

Cornelis Kraaikamp

Bulletin de la Société Mathématique de France (1993)

  • Volume: 121, Issue: 1, page 117-131
  • ISSN: 0037-9484

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Kraaikamp, Cornelis. "Maximal $S$-expansions are Bernoulli shifts." Bulletin de la Société Mathématique de France 121.1 (1993): 117-131. <http://eudml.org/doc/87657>.

@article{Kraaikamp1993,
author = {Kraaikamp, Cornelis},
journal = {Bulletin de la Société Mathématique de France},
keywords = {semi-regular continued fraction; SRCF expansion; dynamical system; nearest integer continued fraction; singularization; maximal - expansion; Bernoulli shift},
language = {eng},
number = {1},
pages = {117-131},
publisher = {Société mathématique de France},
title = {Maximal $S$-expansions are Bernoulli shifts},
url = {http://eudml.org/doc/87657},
volume = {121},
year = {1993},
}

TY - JOUR
AU - Kraaikamp, Cornelis
TI - Maximal $S$-expansions are Bernoulli shifts
JO - Bulletin de la Société Mathématique de France
PY - 1993
PB - Société mathématique de France
VL - 121
IS - 1
SP - 117
EP - 131
LA - eng
KW - semi-regular continued fraction; SRCF expansion; dynamical system; nearest integer continued fraction; singularization; maximal - expansion; Bernoulli shift
UR - http://eudml.org/doc/87657
ER -

References

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  1. [B] BOSMA (W.). — Optimal Continued Fractions, Indag. Math., t. 50, 1988, p. 353-379. Zbl0638.10034
  2. [BK1] BOSMA (W.) and KRAAIKAMP (C.). — Metrical Theory for Optimal Continued Fractions, J. Number Theory, t. 34, 1990, p. 251-270. Zbl0697.10043MR91d:11095
  3. [BK2] BOSMA (W.) and KRAAIKAMP (C.). — Optimal approximation by continued fractions, J. Austral. Math. Soc. Ser. A, t. 50, 1991, p. 481-504. Zbl0731.11038MR92f:11093
  4. [FO] FRIEDMAN (N.A.) and ORNSTEIN (D.S.). — On isomorphisms of weak Bernoulli transformations, Adv. in Math., t. 5, 1970, p. 365-394. Zbl0203.05801MR43 #478c
  5. [K1] KRAAIKAMP (C.). — A new class of continued fraction expansions, Acta Math., t. LVII, 1991, p. 1-39. Zbl0721.11029MR92a:11090
  6. [K2] KRAAIKAMP (C.). — Statistic and ergodic properties of Minkowski's Diagonal Continued Fraction, Theoret. Comput. Sci., t. 65, 1989, p. 197-212. Zbl0671.10029MR90m:11120
  7. [L] LIARDET (P.). — Question posed at the public defence of the dissertation of C. Kraaikamp, Amsterdam, 1990, April 23. 
  8. [NIT] NAKADA (H.), ITO (SH.) and TANAKA (S.). — On the invariant measure for the transformation associated with some real continued fraction, Keio Eng. Rep., t. 30, 1977, p. 159-175. Zbl0412.10037MR58 #16574
  9. [N] NAKADA (H.). — Metrical theory for a class of continued fraction transformations and their natural extensions, Tokyo J. Math., t. 4, 1981, p. 399-426. Zbl0479.10029MR83k:10095
  10. [OW] ORNSTEIN (D.S.) and WEISS (B.). — Statistical Properties of Chaotic Systems, Bull. Amer. Math. Soc., t. 24, 1991, p. 11-116. Zbl0718.58038MR91g:58160
  11. [R] RIEGER (G.J.). — Mischung und Ergodizität bei Kettenbrüchen nach nächsten Ganzen, J. Reine Angew. Math., t. 310, 1979, p. 171-181. Zbl0409.10038MR81c:10066

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