Geodesic
Some results on Poincaré sets
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 891-903

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

It is known that a set $H$ of positive integers is a Poincaré set (also called intersective set, see I. Ruzsa (1982)) if and only if $\dim _{\mathcal {H}}(X_{H})=0$, where $$ X_{H}:=\biggl \{ x=\sum ^{\infty }_{n=1} \frac {x_{n}}{2^{n}} \colon x_{n}\in \{0,1\}, x_{n} x_{n+h}=0 \ \text {for all} \ n\geq 1, \ h\in H\biggr \} $$ and $\dim _{\mathcal {H}}$ denotes the Hausdorff dimension (see C. Bishop, Y. Peres (2017), Theorem 2.5.5). In this paper we study the set $X_H$ by replacing $2$ with $b>2$. It is surprising that there are some new phenomena to be worthy of studying. We study them and give several examples to explain our results.
DOI : 10.21136/CMJ.2020.0001-19
Classification : 11A07, 37B20
Keywords: Poincaré set; homogeneous set; Hausdorff dimension 
@article{10_21136_CMJ_2020_0001_19,
     author = {Tang, Min-wei and Wu, Zhi-Yi},
     title = {Some results on {Poincar\'e} sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {891--903},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {2020},
     doi = {10.21136/CMJ.2020.0001-19},
     mrnumber = {4151712},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0001-19/}
}
TY  - JOUR
AU  - Tang, Min-wei
AU  - Wu, Zhi-Yi
TI  - Some results on Poincaré sets
JO  - Czechoslovak Mathematical Journal
PY  - 2020
SP  - 891
EP  - 903
VL  - 70
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0001-19/
DO  - 10.21136/CMJ.2020.0001-19
LA  - en
ID  - 10_21136_CMJ_2020_0001_19
ER  - 
%0 Journal Article
%A Tang, Min-wei
%A Wu, Zhi-Yi
%T Some results on Poincaré sets
%J Czechoslovak Mathematical Journal
%D 2020
%P 891-903
%V 70
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0001-19/
%R 10.21136/CMJ.2020.0001-19
%G en
%F 10_21136_CMJ_2020_0001_19
Tang, Min-wei; Wu, Zhi-Yi. Some results on Poincaré sets. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 891-903. doi: 10.21136/CMJ.2020.0001-19

Cité par Sources :