Geodesic
On the set of subarcs in some non-postrcritically finite dendrites
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 975-982.

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct a family ${\mathbf F}$ of non-PCF dendrites $K$ in a plane, such that for any dendrite $K\in {\mathbf F}$ all its subarcs have the same Hausdorff dimension $s$, while the set of $s$-dimensional Hausdorff measures of subarcs connecting the given point and a self-similar Cantor subset in $K$ is a Cantor discontinuum.
Keywords: self-similar dendrite, postcritically finite set.
Mots-clés : ramification point, Hausdorff dimension 
@article{SEMR_2019_16_a57,
     author = {N. V. Abrosimov and M. V. Chanchieva and A. V. Tetenov},
     title = {On the set of subarcs in some non-postrcritically finite dendrites},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {975--982},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a57/}
}
TY  - JOUR
AU  - N. V. Abrosimov
AU  - M. V. Chanchieva
AU  - A. V. Tetenov
TI  - On the set of subarcs in some non-postrcritically finite dendrites
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 975
EP  - 982
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a57/
LA  - en
ID  - SEMR_2019_16_a57
ER  - 
%0 Journal Article
%A N. V. Abrosimov
%A M. V. Chanchieva
%A A. V. Tetenov
%T On the set of subarcs in some non-postrcritically finite dendrites
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 975-982
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a57/
%G en
%F SEMR_2019_16_a57
N. V. Abrosimov; M. V. Chanchieva; A. V. Tetenov. On the set of subarcs in some non-postrcritically finite dendrites. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 975-982. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a57/

[1] C. Bandt, J. Stahnke, Self-similar sets 6. Interior distance on deterministic fractals, preprint, Greifswald, 1990 | MR | Zbl

[2] L.L. Cristea, B. Steinsky, “Curves of infinite length in labyrinth fractals”, Proc. Edinb. Math. Soc., II. Ser., 54:2 (2011), 329–344 | DOI | MR | Zbl

[3] J. Kigami,, Analysis on fractals, Cambridge Tracts in Mathematics, 143, Cambridge University Press, Cambridge, 2001 | MR | Zbl

[4] R.D. Mauldin, S.C. Williams, “Hausdorff dimension in graph directed constructions”, Trans. Am. Math. Soc., 309:2 (1988), 811–829 | DOI | MR | Zbl

[5] P. Singh, A.V. Tetenov, “A self-similar dendrite with one-point intersection and infinite post-critical set”, Adv. Theory Nonlinear Anal. Appl., 2:2 (2018), 70–73 | Zbl

[6] M. Samuel, A.V. Tetenov, D.A. Vaulin, “Self-similar dendrites generated by polygonal systems in the plane”, Siberian Electronic Mathematical Reports, 14 (2017), 737–751 | MR | Zbl

[7] R. Strichartz,, Differential equations on fractals: a tutorial, Princeton University Press, Princeton, 2006 | MR | Zbl

[8] A.V. Tetenov, M. Samuel, D.A. Vauilin, “On dendrites generated by polyhedral systems and their ramification points”, Trudy Inst. Mat. Mekh. UrO RAN, 23, no. 4, 2017, 281–291 | DOI | MR