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dc.contributor.author
Shmerkin, Pablo Sebastian
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dc.date.available
2019-05-27T19:11:04Z
dc.date.issued
2017-05
dc.identifier.citation
Shmerkin, Pablo Sebastian; On distance sets, box-counting and Ahlfors regular sets; Alliance of Diamond Open Access Journals; Discrete Analysis; 2017; 9; 5-2017; 1-22
dc.identifier.issn
2397-3129
dc.identifier.uri
http://hdl.handle.net/11336/77253
dc.description.abstract
We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent s > 1. As a corollary, we improve upon a recent result of Orponen, by showing that if A is Ahlfors-regular of dimension s > 1, then almost all pinned distance sets of A have lower box-counting dimension 1. We also show that if A,B ⊂ R 2 have Hausdorff dimension greater than 1 and A is Ahlfors-regular, then the set of distances between A and B has modified lower box-counting dimension 1, which taking B = A improves Orponen’s result in a different direction, by lowering packing dimension to modified lower box-counting dimension. The proofs involve ergodic-theoretic ideas, relying on the theory of CP-processes and projections.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Alliance of Diamond Open Access Journals
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Distance Sets
dc.subject
Box Dimension
dc.subject
Ahlfors-Regular Sets
dc.subject
Cp-Processes
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
On distance sets, box-counting and Ahlfors regular sets
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-05-23T14:02:02Z
dc.journal.volume
2017
dc.journal.number
9
dc.journal.pagination
1-22
dc.journal.pais
Reino Unido
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dc.journal.ciudad
Cambridge
dc.description.fil
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
dc.journal.title
Discrete Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://discreteanalysisjournal.com/article/1643-on-distance-sets-box-counting-and-ahlfors-regular-set
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.19086/da.1643
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/arXiv:1605.00187
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