Correlation dimension for self-similar Cantor sets with overlaps

Károly Simon; Boris Solomyak

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 3, page 293-300
  • ISSN: 0016-2736

Abstract

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We prove a classification theorem of the “Glimm-Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order ≤ 0 which is not Borel linearizable.

How to cite

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Simon, Károly, and Solomyak, Boris. "Correlation dimension for self-similar Cantor sets with overlaps." Fundamenta Mathematicae 155.3 (1998): 293-300. <http://eudml.org/doc/212257>.

@article{Simon1998,
abstract = {We prove a classification theorem of the “Glimm-Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order $≤_0$ which is not Borel linearizable.},
author = {Simon, Károly, Solomyak, Boris},
journal = {Fundamenta Mathematicae},
keywords = {Borel partial order; Borel linear order; self-similar set; address map; thickness; correlation dimension; iterated function system; similarity dimension; attractor; IFS; box counting dimension},
language = {eng},
number = {3},
pages = {293-300},
title = {Correlation dimension for self-similar Cantor sets with overlaps},
url = {http://eudml.org/doc/212257},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Simon, Károly
AU - Solomyak, Boris
TI - Correlation dimension for self-similar Cantor sets with overlaps
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 3
SP - 293
EP - 300
AB - We prove a classification theorem of the “Glimm-Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order $≤_0$ which is not Borel linearizable.
LA - eng
KW - Borel partial order; Borel linear order; self-similar set; address map; thickness; correlation dimension; iterated function system; similarity dimension; attractor; IFS; box counting dimension
UR - http://eudml.org/doc/212257
ER -

References

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  1. [1] L. A. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), 903-928. Zbl0778.28011
  2. [2] L. A. Harrington, D. Marker and S. Shelah, Borel orderings, Trans. Amer. Math. Soc. 310 (1988), 293-302. 

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