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

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.