Artículo
Cabrelli, C.A.; Hare, K.E.; Molter, U.M. "Sums of Cantor sets yielding an interval" (2002) Journal of the Australian Mathematical Society. 73(3):405-418
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Abstract:
In this paper we prove that if a Cantor set has ratios of dissection bounded away from zero, then there is a natural number N, such that its N-fold sum is an interval. Moreover, for each element z of this interval, we explicitly construct the N elements of C whose sum yields z. We also extend a result of Mendes and Oliveira showing that when s is irrational Ca + Cas is an interval if and only if a/(1 - 2a) as/(1 - 2as) ≥ 1.
Registro:
| Documento: | Artículo |
| Título: | Sums of Cantor sets yielding an interval |
| Autor: | Cabrelli, C.A.; Hare, K.E.; Molter, U.M. |
| Filiación: | Departamento de Matematica FCEyN, Universidad de Buenos Aires, Cdad. Universitaria, Pab. I, 1428 Buenos Aires, Argentina Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada |
| Palabras clave: | Cantor set; Sums of sets |
| Año: | 2002 |
| Volumen: | 73 |
| Número: | 3 |
| Página de inicio: | 405 |
| Página de fin: | 418 |
| Título revista: | Journal of the Australian Mathematical Society |
| Título revista abreviado: | J. Aust. Math. Soc. |
| ISSN: | 14467887 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v73_n3_p405_Cabrelli |
Referencias:
- Astels, S., Cantor sets and numbers with restricted partial quotients (2000) Trans. Amer. Math. Soc., 352, pp. 133-170
- Bamon, R., Plaza, S., Vera, J., On central Cantor sets with self-arithmetic difference of positive Lebesgue measure (1995) J. London Math. Soc., 52, pp. 137-146
- Brown, G., Keane, M., Moran, W., Pearce, E., An inequality, with applications to Cantor measures and normal numbers (1988) Mathematika, 35, pp. 87-94
- Brown, G., Moran, W., Raikov systems and radicals in convolution measure algebras (1983) J. London Math. Soc., 28, pp. 531-542
- Cabrelli, C., Hare, K., Molter, U., Sums of Cantor sets (1997) Ergodic Theory Dynam. Systems, 17, pp. 1299-1313
- Hall M., Jr., On the sum and product of continued fractions (1947) Ann. of Math. (2), 48, pp. 966-993
- Mendes, P., Oliveira, F., On the topological structure of the arithmetic sum of two Cantor sets (1994) Nonlinearity, 7, pp. 329-343
- Moreira, C., Yoccoz, J., Stable intersections of Cantor sets with large Hausdofff dimension (2001) Ann. of Math. (2), 154, pp. 45-96
- Newhouse, S., Lectures on dynamical systems (1980) Progress in Math., 8, pp. 1-114. , Dynamical systems, CIME Lectures, Bressanone, Italy, 1978 (Birkhauser, Boston, Mass.)
- Palis, J., Takens, F., Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations (1993) Cambridge Stud. Adv. Math., 35. , Cambridge University Press, Cambridge
- Salem, R., On sets of multiplicity for trigonometric series (1942) Amer. J. Math., 64, pp. 531-538
- Sannami, A., An example of a regular Cantor set whose difference set is a Cantor set with positive measure (1992) Hokkaido Math. J., 21, pp. 7-24
Citas:
---------- APA ----------
Cabrelli, C.A., Hare, K.E. & Molter, U.M. (2002) . Sums of Cantor sets yielding an interval. Journal of the Australian Mathematical Society, 73(3), 405-418.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v73_n3_p405_Cabrelli [ ]
---------- CHICAGO ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. "Sums of Cantor sets yielding an interval" . Journal of the Australian Mathematical Society 73, no. 3 (2002) : 405-418.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v73_n3_p405_Cabrelli [ ]
---------- MLA ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. "Sums of Cantor sets yielding an interval" . Journal of the Australian Mathematical Society, vol. 73, no. 3, 2002, pp. 405-418.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v73_n3_p405_Cabrelli [ ]
---------- VANCOUVER ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. Sums of Cantor sets yielding an interval. J. Aust. Math. Soc. 2002;73(3):405-418.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v73_n3_p405_Cabrelli [ ]
