Artículo
Cabrelli, C.A.; Hare, K.E.; Molter, U.M. "Classifying cantor sets by their fractal dimensions" (2010) Proceedings of the American Mathematical Society. 138(11):3965-3974
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Classifying cantor sets by their fractal dimensions |
| Autor: | Cabrelli, C.A.; Hare, K.E.; Molter, U.M. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada |
| Palabras clave: | Cantor set; Cut-out set; Hausdorff dimension; Packing dimension |
| Año: | 2010 |
| Volumen: | 138 |
| Número: | 11 |
| Página de inicio: | 3965 |
| Página de fin: | 3974 |
| DOI: | http://dx.doi.org/10.1090/S0002-9939-2010-10396-9 |
| Título revista: | Proceedings of the American Mathematical Society |
| Título revista abreviado: | Proc. Am. Math. Soc. |
| ISSN: | 00029939 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v138_n11_p3965_Cabrelli |
Referencias:
- Besicovitch, A.S., Taylor, S.J., On the complementary intervals of a linear closed set of zero Lebesgue measure (1954) J. London Math. Soc., 29, pp. 449-459. , MR0064849 (16:344d)
- Cabrelli, C., Mendivil, F., Molter, U., Shonkwiler, R., On the h-Hausdorff measure of Cantor sets (2004) Pac. J. of Math., 217, pp. 29-43. , MR2105765 (2005h:28013)
- Cabrelli, C., Molter, U., Paulauskas, V., Shonkwiler, R., The hausdorff dimension of p- Cantor sets (2004) Real Anal. Exchange, 30 (2), pp. 413-433. , MR2177411 (2006g:28012),2005
- Falconer, K., (1997) Techniques in Fractal Geometry, , Wiley and Sons Chichester,MR1449135 (99f:28013)
- Garcia, I., Molter, U., Scotto, R., Dimension functions of Cantor sets (2007) Proc. Amer. Math. Soc., 135, pp. 3151-3161. , MR2322745 (2008i:28004)
- Rogers, C.A., (1998) Hausdorff Measures Cambridge Math Library, , Cambridge University Press Cambridge,MR1692618 (2000b:28009)
- Tricot, C., Two definitions of fractional dimension (1982) Math. Proc. Camb. Phil. Soc., 91, pp. 57-74. , MR633256 (84d:28013)
- Taylor, S.J., Tricot, C., Packing measure and its evaluation for a Brownian path (1985) Trans. Amer. Math. Soc., 288, pp. 679-699. , MR776398 (87a:28002)
Citas:
---------- APA ----------
Cabrelli, C.A., Hare, K.E. & Molter, U.M. (2010) . Classifying cantor sets by their fractal dimensions. Proceedings of the American Mathematical Society, 138(11), 3965-3974.http://dx.doi.org/10.1090/S0002-9939-2010-10396-9
---------- CHICAGO ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. "Classifying cantor sets by their fractal dimensions" . Proceedings of the American Mathematical Society 138, no. 11 (2010) : 3965-3974.http://dx.doi.org/10.1090/S0002-9939-2010-10396-9
---------- MLA ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. "Classifying cantor sets by their fractal dimensions" . Proceedings of the American Mathematical Society, vol. 138, no. 11, 2010, pp. 3965-3974.http://dx.doi.org/10.1090/S0002-9939-2010-10396-9
---------- VANCOUVER ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. Classifying cantor sets by their fractal dimensions. Proc. Am. Math. Soc. 2010;138(11):3965-3974.http://dx.doi.org/10.1090/S0002-9939-2010-10396-9
