Sums of Cantor sets yielding an interval
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 resu...
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2002
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| LEADER | 03932caa a22004697a 4500 | ||
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| 003 | AR-BaUEN | ||
| 005 | 20230518203445.0 | ||
| 008 | 190411s2002 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0036921654 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Cabrelli, C.A. | |
| 245 | 1 | 0 | |a Sums of Cantor sets yielding an interval |
| 260 | |c 2002 | ||
| 270 | 1 | 0 | |m Cabrelli, C.A.; Departamento de Matematica FCEyN, Universidad de Buenos Aires, Cdad. Universitaria, Pab. I, 1428 Buenos Aires, Argentina; email: ccabrelli@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Astels, S., Cantor sets and numbers with restricted partial quotients (2000) Trans. Amer. Math. Soc., 352, pp. 133-170 | ||
| 504 | |a 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 | ||
| 504 | |a Brown, G., Keane, M., Moran, W., Pearce, E., An inequality, with applications to Cantor measures and normal numbers (1988) Mathematika, 35, pp. 87-94 | ||
| 504 | |a Brown, G., Moran, W., Raikov systems and radicals in convolution measure algebras (1983) J. London Math. Soc., 28, pp. 531-542 | ||
| 504 | |a Cabrelli, C., Hare, K., Molter, U., Sums of Cantor sets (1997) Ergodic Theory Dynam. Systems, 17, pp. 1299-1313 | ||
| 504 | |a Hall M., Jr., On the sum and product of continued fractions (1947) Ann. of Math. (2), 48, pp. 966-993 | ||
| 504 | |a Mendes, P., Oliveira, F., On the topological structure of the arithmetic sum of two Cantor sets (1994) Nonlinearity, 7, pp. 329-343 | ||
| 504 | |a Moreira, C., Yoccoz, J., Stable intersections of Cantor sets with large Hausdofff dimension (2001) Ann. of Math. (2), 154, pp. 45-96 | ||
| 504 | |a Newhouse, S., Lectures on dynamical systems (1980) Progress in Math., 8, pp. 1-114. , Dynamical systems, CIME Lectures, Bressanone, Italy, 1978 (Birkhauser, Boston, Mass.) | ||
| 504 | |a Palis, J., Takens, F., Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations (1993) Cambridge Stud. Adv. Math., 35. , Cambridge University Press, Cambridge | ||
| 504 | |a Salem, R., On sets of multiplicity for trigonometric series (1942) Amer. J. Math., 64, pp. 531-538 | ||
| 504 | |a 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 | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Departamento de Matematica FCEyN, Universidad de Buenos Aires, Cdad. Universitaria, Pab. I, 1428 Buenos Aires, Argentina | ||
| 593 | |a Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada | ||
| 690 | 1 | 0 | |a CANTOR SET |
| 690 | 1 | 0 | |a SUMS OF SETS |
| 700 | 1 | |a Hare, K.E. | |
| 700 | 1 | |a Molter, U.M. | |
| 773 | 0 | |d 2002 |g v. 73 |h pp. 405-418 |k n. 3 |p J. Aust. Math. Soc. |x 14467887 |t Journal of the Australian Mathematical Society | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-0036921654&partnerID=40&md5=dde27e901a9ee437c4cdb4d9a23f8068 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_14467887_v73_n3_p405_Cabrelli |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v73_n3_p405_Cabrelli |y Registro en la Biblioteca Digital |
| 961 | |a paper_14467887_v73_n3_p405_Cabrelli |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 66081 | ||