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ArticleOriginal scientific text

Title

Minimal self-joinings and positive topological entropy II

Authors 1, 2

Affiliations

  1. CNRS-LMD, Case 930, 163 avenue de Luminy, 13288 Marseille Cedex 09, France
  2. Faculty of Mathematics and Computer Science, Nicolas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

An effective construction of positive-entropy almost one-to-one topological extensions of the Chacón flow is given. These extensions have the property of almost minimal power joinings. For each possible value of entropy there are uncountably many pairwise non-conjugate such extensions.

Keywords

ENG
topological coalescence, self-joinings, topological entropy

Bibliography

  1. [BIGlKw] F. Blanchard, E. Glasner and J. Kwiatkowski, Minimal self-joinings and positive topological entropy, Monatsh. Math. 120 (1995), 205-222.
  2. [BuKw] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropy, Studia Math. 103 (1992), 133-142.
  3. [Cha] R. V. Chacón, A geometric construction of measure preserving transformations, in: Proc. Fifth Berkeley Sympos. Math. Statist. and Probab., Vol. II, Part 2, Univ. of California Press, 1965, 335-360.
  4. [DeGrSi] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, Berlin, 1975.
  5. [Gri] C. Grillenberger, Constructions of strictly ergodic systems: I. Given entropy, Z. Wahrsch. Verw. Gebiete 25 (1973), 323-334.
  6. [delJ] A. del Junco, On minimal self-joinings in topological dynamics, Ergodic Theory Dynam. Systems 7 (1987), 211-227.
  7. [delJKe] A. del Junco and M. Keane, On generic points in the Cartesian square of Chacón's transformation, ibid. 5 (1985), 59-69.
  8. [delJRaSw] A. del Junco, A. M. Rahe and L. Swanson, Chacón's automorphism has minimal self-joinings, J. Analyse Math. 37 (1980), 276-284.
  9. [King] J. King, A map with topological minimal self-joinings in the sense of del Junco, Ergodic Theory Dynam. Systems 10 (1990), 745-761.
  10. [Mar] N. Markley, Topological minimal self-joinings, ibid. 3 (1983), 579-599.
  11. [New] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136.
  12. [Rud] D. J. Rudolph, An example of a measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122.
  13. [Wal] P. Walters, Affine transformations and coalescence, Math. Systems Theory 8 (1974), 33-44.
Studia Mathematica
1998/128/2
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Pages:
121-133
Main language of publication
English
Received
1996-09-12
Accepted
1997-09-08
Published
1998
Exact and natural sciences