Do self-similar sets with positive Lebesgue measure contain an interval?
Tài liệu tham khảo
Palis, 1993
Mendes, 1994, On the topological structure of the arithmetic sum of two Cantor sets, Nonlinearity, 7, 324, 10.1088/0951-7715/7/2/002
Bandt, 1992, Self-similar sets 7: A characterization of self-similar fractals with positive Hausdorff measure, Proc. Amer. Math. Soc., 114, 995
Kenyon, 1992, Self-replicating tilings, vol. 135, 239
Schief, 1994, Separation properties for self-similar sets, Proc. Amer. Math. Soc., 122, 111, 10.1090/S0002-9939-1994-1191872-1
Mandelbrot, 1977
Bandt, 1991, Self-similar sets 5, integer matrices and tilings of Rn, Proc. Amer. Math. Soc., 112, 549
Bandt, 2004, Distribution of distances and interior distances for certain self- certain measures, Arab. J. Sci. Eng., 29–2C, 111
Edgar, 1990
Falconer, 1990
Hata, 1985, On the structure of self-similar sets, Japan J. Appl. Math., 2, 381, 10.1007/BF03167083
Hutchinson, 1981, Fractals and self-similarity, Indiana Univ. Math. J., 30, 713, 10.1512/iumj.1981.30.30055
Lalley, 1988, The packing and covering function of some self-similar fractals, Indiana Univ. Math. J., 37, 699, 10.1512/iumj.1988.37.37034
Zerner, 1996, Weak separation properties for self-similar sets, Proc. Amer. Math. Soc., 124, 3529, 10.1090/S0002-9939-96-03527-7
Balogh, 2005, Hausdorff dimensions of self-similar and self-affine fractals in the Heisenberg group, Proc. London Math. Soc., 91, 153, 10.1112/S0024611504015205
Lau, 2005, Some exceptional phenomena in multifractal formalism, Asian J. Math., 9, 275, 10.4310/AJM.2005.v9.n2.a13
Shang, 2001, Hausdorff measure and dimension of some fractals in RN, Nonlinear Anal., 45, 817, 10.1016/S0362-546X(99)00411-3
Shang, 2000, Is the Hausdorff dimension of a set and its image equal under binary coding map, Chaos Solitons Fractals, 11, 1093, 10.1016/S0960-0779(99)00013-2
Shang, 2001, Fractal dimension of quasi-periodic orbits, Appl. Math. Letters, 14, 969, 10.1016/S0893-9659(01)00073-8
Shang, 2004, Fractal properties of de Rham-type curve associated to random walk, Chaos Solitons Fractals, 21, 695, 10.1016/j.chaos.2003.12.099
Shang, 2004, Power series and open set condition of Hutchinson, J. Phys. A, 37, 1219, 10.1088/0305-4470/37/4/009
Moran, 1946, Additive functions of intervals and Hausdorff measure, Proc. Cambridge Philos. Soc., 42, 15, 10.1017/S0305004100022684
Williams, 1971, Composition of contractions, Bol. Soc. Brasil. Mat., 2, 55, 10.1007/BF02584684
Berger, 1992, Multidimensional two-scale dilation equations, 295
Debnath, 2006, A brief historical introduction to fractals and fractal geometry, Int. J. Math. Educ. Sci. Technol., 37, 29, 10.1080/00207390500186206
Drenning, 2005, Outer boundaries of self-similar tiles, Experiment. Math., 14, 199, 10.1080/10586458.2005.10128919
Stein, 1970