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dc.contributor.author
Becher, Veronica Andrea
dc.contributor.author
Reimann, Jan
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Slaman, Theodore A.
dc.date.available
2020-02-10T20:33:39Z
dc.date.issued
2018-02
dc.identifier.citation
Becher, Veronica Andrea; Reimann, Jan; Slaman, Theodore A.; Irrationality exponent, Hausdorff dimension and effectivization; Springer Wien; Monatshefete Fur Mathematik; 185; 2; 2-2018; 167-188
dc.identifier.issn
0026-9255
dc.identifier.uri
http://hdl.handle.net/11336/97123
dc.description.abstract
We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension and show that the two notions are independent. For any real number a greater than or equal to 2 and any non-negative real b be less than or equal to 2 / a, we show that there is a Cantor-like set with Hausdorff dimension equal to b such that, with respect to its uniform measure, almost all real numbers have irrationality exponent equal to a. We give an analogous result relating the irrationality exponent and the effective Hausdorff dimension of individual real numbers. We prove that there is a Cantor-like set such that, with respect to its uniform measure, almost all elements in the set have effective Hausdorff dimension equal to b and irrationality exponent equal to a. In each case, we obtain the desired set as a distinguished path in a tree of Cantor sets.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer Wien
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
CANTOR SETS
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DIOPHANTINE APPROXIMATION
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EFFECTIVE HAUSDORFF DIMENSION
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Ciencias de la Computación
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Ciencias de la Computación e Información
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CIENCIAS NATURALES Y EXACTAS
dc.title
Irrationality exponent, Hausdorff dimension and effectivization
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-12-16T19:15:41Z
dc.journal.volume
185
dc.journal.number
2
dc.journal.pagination
167-188
dc.journal.pais
Austria
dc.journal.ciudad
Viena
dc.description.fil
Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
dc.description.fil
Fil: Reimann, Jan. State University of Pennsylvania; Estados Unidos
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Fil: Slaman, Theodore A.. University of California. Department of Mathematics; Estados Unidos
dc.journal.title
Monatshefete Fur Mathematik
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00605-017-1094-2
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info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1007/s00605-017-1094-2
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1601.00153
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