Abstract:
We find conditions on the ratios of dissection of a Cantor set so that the group it generates under addition has positive Lebesgue measure. In particular, we answer affirmatively a special case of a conjecture posed by J. Palis.
Registro:
Documento: |
Artículo
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Título: | Sums of Cantor sets |
Autor: | Cabrelli, C.A.; Hare, K.E.; Molter, U.M. |
Filiación: | Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pab. I, (1428) Bs.As., Argentina Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada
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Año: | 1997
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Volumen: | 17
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Número: | 6
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Página de inicio: | 1299
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Página de fin: | 1313
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DOI: |
http://dx.doi.org/10.1017/S0143385797097678 |
Título revista: | Ergodic Theory and Dynamical Systems
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Título revista abreviado: | Ergodic Theory Dyn. Syst.
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ISSN: | 01433857
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01433857_v17_n6_p1299_Cabrelli |
Referencias:
- Bamón, R., Plaza, S., Vera, J., On central Cantor sets with self-arithmetic difference of positive lebesgue measure (1995) J. London Math. Soc., 52 (2), pp. 137-146
- Boas R.P., Jr., (1960) A Primer of Real Functions (The Carus Mathematical Monographs), , The Mathematical Association of America, Washington, D.C
- Brown, G., Keane, M.S., Moran, W., Pearce, C.E.M., 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., 2 (28), pp. 531-542
- Dubuc, E.J., (1994), Private Communication; Falconer, K.J., (1990) Fractal Geometry, Mathematical Foundations and Applications, , John Wiley & Sons
- Kraft, R.L., Intersections of thick Cantor sets (1992) Mem. Amer. Math. Soc., 97 (468)
- Mendes, P., Oliveira, F., On the topological structure of the arithmetic sum of two Cantor sets (1994) Nonlinearity, 7, pp. 329-343
- Newhouse, S.E., Lectures on dynamical systems (1980) Dynamical Systems, C.I.M.E. Lectures (Bressanoe, Italy, 1978) Progress in Mathematics, 8, pp. 1-114. , Birkhäuser
- Palis, J., Takens, F., (1993) Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations Studies in Advanced Mathematics, 35. , Cambridge University Press
- Salem, R., On sets of multiplicity for trigonometrical 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
- Steinhaus, H., Nowa wlasność mnogości G. Cantora (1916) Wektor, 6, pp. 105-107
- (1985) Hugo Steinhaus: Selected Papers, , Polish Scientific Publishers
Citas:
---------- APA ----------
Cabrelli, C.A., Hare, K.E. & Molter, U.M.
(1997)
. Sums of Cantor sets. Ergodic Theory and Dynamical Systems, 17(6), 1299-1313.
http://dx.doi.org/10.1017/S0143385797097678---------- CHICAGO ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M.
"Sums of Cantor sets"
. Ergodic Theory and Dynamical Systems 17, no. 6
(1997) : 1299-1313.
http://dx.doi.org/10.1017/S0143385797097678---------- MLA ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M.
"Sums of Cantor sets"
. Ergodic Theory and Dynamical Systems, vol. 17, no. 6, 1997, pp. 1299-1313.
http://dx.doi.org/10.1017/S0143385797097678---------- VANCOUVER ----------
Cabrelli, C.A., Hare, K.E., Molter, U.M. Sums of Cantor sets. Ergodic Theory Dyn. Syst. 1997;17(6):1299-1313.
http://dx.doi.org/10.1017/S0143385797097678