Classifying cantor sets by their fractal dimensions

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequ...

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Autores principales: Cabrelli, C.A., Hare, K.E., Molter, U.M.
Formato: JOUR
Materias:
Cantor set
Cut-out set
Hausdorff dimension
Packing dimension
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v138_n11_p3965_Cabrelli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00029939_v138_n11_p3965_Cabrelli
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spelling todo:paper_00029939_v138_n11_p3965_Cabrelli2023-10-03T13:55:10Z Classifying cantor sets by their fractal dimensions Cabrelli, C.A. Hare, K.E. Molter, U.M. Cantor set Cut-out set Hausdorff dimension Packing dimension In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences. © 2010 American Mathematical Society. Fil:Cabrelli, C.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v138_n11_p3965_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cantor set
Cut-out set
Hausdorff dimension
Packing dimension
spellingShingle Cantor set
Cut-out set
Hausdorff dimension
Packing dimension
Cabrelli, C.A.
Hare, K.E.
Molter, U.M.
Classifying cantor sets by their fractal dimensions
topic_facet Cantor set
Cut-out set
Hausdorff dimension
Packing dimension
description In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences. © 2010 American Mathematical Society.
format JOUR
author Cabrelli, C.A.
Hare, K.E.
Molter, U.M.
author_facet Cabrelli, C.A.
Hare, K.E.
Molter, U.M.
author_sort Cabrelli, C.A.
title Classifying cantor sets by their fractal dimensions
title_short Classifying cantor sets by their fractal dimensions
title_full Classifying cantor sets by their fractal dimensions
title_fullStr Classifying cantor sets by their fractal dimensions
title_full_unstemmed Classifying cantor sets by their fractal dimensions
title_sort classifying cantor sets by their fractal dimensions
url http://hdl.handle.net/20.500.12110/paper_00029939_v138_n11_p3965_Cabrelli
work_keys_str_mv AT cabrellica classifyingcantorsetsbytheirfractaldimensions
AT hareke classifyingcantorsetsbytheirfractaldimensions
AT molterum classifyingcantorsetsbytheirfractaldimensions
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