On the arithmetic sum of middle-cantor sets
DOI:
https://doi.org/10.22199/S07160917.1995.0001.00005Abstract
In this article we study the arithmetic sum (difference) set K? + K? in I = [0, 1] in terms of the parameters (?, ?) ? I x I, where K? and K? are middle-Cantor sets contained in I. We describe two regions, A and B, in the parameter space (?, ?) where the characterization of the arithmetic sum set K? + K? is given.
References
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[2] Falconer, K. Fractal Geometry. J., Wiley& Sons (1990).
[3] Falconer, K. The Geometry of Fractal Sets. Cambridge Univ. Press (1985).
[4] Mendes, P., Oliveira, F. On the topological structure of the arithmetic sum of two Cantor sets. Nonlinearity 7, 329-343 (1994).
[5] Newhouse, S. The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms. Publ. Math. !.H. E. S. 50, 101-151 (1979).
[6] Palis, J. Homoclinic orbits, hyperbolic dynamics and dimension of Cantor sets. Contemporary Mathematics vol. 58, part III, 204-216 (1987).
[7] Palis, J., Takens, F. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: fractal dimensions and infinitely many attractors. Cambridge Univ. Press (1993).
[8] Sannami, A. An example of regular Cantor set whose difference is a Cantor set with positive Lebesgue measure. Hokkaido Math. Journal, vol. XXI {1), 7-24 (1992).
[9] Williams, R. F. How big is the intersection of two Cantor sets?. Contemporary Mathematics, vol. 117, 163-175 (1991).
Published
2018-04-03
How to Cite
[1]
E. Muñoz, J. Vera, and S. Plaza, “On the arithmetic sum of middle-cantor sets”, Proyecciones (Antofagasta, On line), vol. 14, no. 1, pp. 51-63, Apr. 2018.
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