Geodesic
Top addresses for a certain family of iterated function system on a segment
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2009), pp. 75-81 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a one-parameter family of iterated function systems on the unit segment. For a fixed address $\tau$ we find the set of parameter values such that $\tau$ is the top address.
Keywords: iterated function systems, attractor, top address, $\beta$-expansion, greedy expansion. 
@article{IVM_2009_9_a7,
     author = {K. B. Igudesman},
     title = {Top addresses for a~certain family of iterated function system on a~segment},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--81},
     year = {2009},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_9_a7/}
}
TY  - JOUR
AU  - K. B. Igudesman
TI  - Top addresses for a certain family of iterated function system on a segment
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 75
EP  - 81
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_9_a7/
LA  - ru
ID  - IVM_2009_9_a7
ER  - 
%0 Journal Article
%A K. B. Igudesman
%T Top addresses for a certain family of iterated function system on a segment
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 75-81
%N 9
%U http://geodesic.mathdoc.fr/item/IVM_2009_9_a7/
%G ru
%F IVM_2009_9_a7
K. B. Igudesman. Top addresses for a certain family of iterated function system on a segment. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2009), pp. 75-81. http://geodesic.mathdoc.fr/item/IVM_2009_9_a7/

[1] Hutchinson J., “Fractals and self similarity”, Indiana Univ. Math. J., 30:5 (1981), 713–747 | DOI | MR | Zbl

[2] Barnsley M. F., “Theory and applications of fractal tops”, Fractals in Engineering: New Trends in Theory and Appl., Springer-Verlag, London, 2005, 3–20

[3] Rényi A., “Representations for real numbers and their ergodic properties”, Acta Math. Hung., 8:3–4 (1957), 477–493 | MR | Zbl

[4] Parry W., “On the $\beta$-expansions of real numbers”, Acta Math. Hung., 11:3–4 (1960), 401–416 | MR | Zbl

[5] Erdős P., “On a family of symmetric bernoulli convolutions”, Amer. J. Math., 61 (1939), 974–976 | DOI | MR | Zbl

[6] Peres Y., Schlag W., Solomyak B., “Sixty years of Bernoulli convolutions”, Fractal geometry and stochastics, II, Proc. of the 2nd conference, Greifswald, 2000, 39–65 | MR | Zbl

[7] Sidorov N., “Almost every number has a continuum of $\beta$-expansions”, Amer. Math. Monthly, 110:9 (2003), 838–842 | DOI | MR | Zbl

[8] Barnsley M. F., Superfractals, Cambridge University Press, Cambridge, 2006, 464 pp. | Zbl