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

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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/}
}
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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/