Minimal self-joinings and positive topological entropy II

François Blanchard; Jan Kwiatkowski

Studia Mathematica (1998)

  • Volume: 128, Issue: 2, page 121-133
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Blanchard, François, and Kwiatkowski, Jan. "Minimal self-joinings and positive topological entropy II." Studia Mathematica 128.2 (1998): 121-133. <http://eudml.org/doc/216478>.

@article{Blanchard1998,
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.},
author = {Blanchard, François, Kwiatkowski, Jan},
journal = {Studia Mathematica},
keywords = {topological coalescence; self-joinings; topological entropy; positive-entropy almost one-to-one extensions; Chacon flow},
language = {eng},
number = {2},
pages = {121-133},
title = {Minimal self-joinings and positive topological entropy II},
url = {http://eudml.org/doc/216478},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Blanchard, François
AU - Kwiatkowski, Jan
TI - Minimal self-joinings and positive topological entropy II
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 2
SP - 121
EP - 133
AB - 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.
LA - eng
KW - topological coalescence; self-joinings; topological entropy; positive-entropy almost one-to-one extensions; Chacon flow
UR - http://eudml.org/doc/216478
ER -

References

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  1. [BIGlKw] F. Blanchard, E. Glasner and J. Kwiatkowski, Minimal self-joinings and positive topological entropy, Monatsh. Math. 120 (1995), 205-222. Zbl0859.54027
  2. [BuKw] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropy, Studia Math. 103 (1992), 133-142. Zbl0816.58028
  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. Zbl0328.28008
  5. [Gri] C. Grillenberger, Constructions of strictly ergodic systems: I. Given entropy, Z. Wahrsch. Verw. Gebiete 25 (1973), 323-334. Zbl0253.28004
  6. [delJ] A. del Junco, On minimal self-joinings in topological dynamics, Ergodic Theory Dynam. Systems 7 (1987), 211-227. Zbl0635.54020
  7. [delJKe] A. del Junco and M. Keane, On generic points in the Cartesian square of Chacón's transformation, ibid. 5 (1985), 59-69. Zbl0575.28010
  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. Zbl0445.28014
  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. Zbl0726.28014
  10. [Mar] N. Markley, Topological minimal self-joinings, ibid. 3 (1983), 579-599. Zbl0562.54057
  11. [New] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. Zbl0425.28012
  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. Zbl0446.28018
  13. [Wal] P. Walters, Affine transformations and coalescence, Math. Systems Theory 8 (1974), 33-44. Zbl0299.22008

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