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dc.contributor.author
Morris, Ian D.
dc.contributor.author
Shmerkin, Pablo Sebastian
dc.date.available
2022-11-15T14:27:33Z
dc.date.issued
2018-10
dc.identifier.citation
Morris, Ian D.; Shmerkin, Pablo Sebastian; On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems; American Mathematical Society; Transactions of the American Mathematical Society; 371; 3; 10-2018; 1547-1582
dc.identifier.issn
0002-9947
dc.identifier.uri
http://hdl.handle.net/11336/177835
dc.description.abstract
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-affine proper subsets of the original set. These self-affine subsets may be chosen so as to have stronger separation properties and in such a way that the linear parts of their affinities are positive matrices. Combining this result with some recent breakthroughs in the study of self-affine measures and their associated Furstenberg measures, we obtain new criteria under which the Hausdorff dimension of a self-affine set equals its affinity dimension. For example, applying recent results of Bárány, Hochman–Solomyak, and Rapaport, we provide many new explicit examples of self-affine sets whose Hausdorff dimension equals its affinity dimension, and for which the linear parts do not satisfy any positivity or domination assumptions.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Mathematical Society
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Self-affine sets
dc.subject
Affinity dimension
dc.subject
Hausdorff dimension
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-11-14T11:18:01Z
dc.identifier.eissn
1088-6850
dc.journal.volume
371
dc.journal.number
3
dc.journal.pagination
1547-1582
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Providence
dc.description.fil
Fil: Morris, Ian D.. University of Surrey; Reino Unido
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
Transactions of the American Mathematical Society
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2019-371-03/S0002-9947-2018-07334-2/home.html
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1090/tran/7334
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1602.08789
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