Geodesic
The Hausdorff dimension of the projections of self-affine carpets
Andrew Ferguson 1   ; Thomas Jordan 2   ; Pablo Shmerkin 3
1 Mathematics Institute Zeeman Building University of Warwick Coventry CV4 7AL, UK
2 Department of Mathematics University of Bristol University Walk, Clifton Bristol BS8 1TW, UK
3 School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis Alan Turing Building University of Manchester Oxford Road, Manchester M13 9PL, UK
Fundamenta Mathematicae, Tome 209 (2010) no. 3, pp. 193-213 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if ${\mit\Lambda} $ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of ${\mit\Lambda} $ in a non-principal direction has Hausdorff dimension $\min (\gamma ,1)$, where $\gamma $ is the Hausdorff dimension of ${\mit\Lambda} $. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.
DOI : 10.4064/fm209-3-1
Keywords: study orthogonal projections large class self affine carpets which contains carpets bedford mcmullen special cases main result mit lambda carpet certain natural irrationality conditions every orthogonal projection mit lambda non principal direction has hausdorff dimension min gamma where gamma hausdorff dimension mit lambda generalizes recent result peres shmerkin sums cantor sets

Andrew Ferguson  1   ; Thomas Jordan  2   ; Pablo Shmerkin  3

1 Mathematics Institute Zeeman Building University of Warwick Coventry CV4 7AL, UK
2 Department of Mathematics University of Bristol University Walk, Clifton Bristol BS8 1TW, UK
3 School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis Alan Turing Building University of Manchester Oxford Road, Manchester M13 9PL, UK 
@article{10_4064_fm209_3_1,
     author = {Andrew Ferguson and Thomas Jordan and Pablo Shmerkin},
     title = {The {Hausdorff} dimension of the projections
 of self-affine carpets},
     journal = {Fundamenta Mathematicae},
     pages = {193--213},
     year = {2010},
     volume = {209},
     number = {3},
     doi = {10.4064/fm209-3-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm209-3-1/}
}
TY  - JOUR
AU  - Andrew Ferguson
AU  - Thomas Jordan
AU  - Pablo Shmerkin
TI  - The Hausdorff dimension of the projections
 of self-affine carpets
JO  - Fundamenta Mathematicae
PY  - 2010
SP  - 193
EP  - 213
VL  - 209
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm209-3-1/
DO  - 10.4064/fm209-3-1
LA  - en
ID  - 10_4064_fm209_3_1
ER  - 
%0 Journal Article
%A Andrew Ferguson
%A Thomas Jordan
%A Pablo Shmerkin
%T The Hausdorff dimension of the projections
 of self-affine carpets
%J Fundamenta Mathematicae
%D 2010
%P 193-213
%V 209
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/fm209-3-1/
%R 10.4064/fm209-3-1
%G en
%F 10_4064_fm209_3_1
Andrew Ferguson; Thomas Jordan; Pablo Shmerkin. The Hausdorff dimension of the projections
 of self-affine carpets. Fundamenta Mathematicae, Tome 209 (2010) no. 3, pp. 193-213. doi: 10.4064/fm209-3-1

Cité par Sources :