Artículo
Piacquadio Losada, M.; Grynberg, S. "Cantor staircases in physics and diophantine approximations" (1998) International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 8(6):1095-1106
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Abstract:
For a wide class of dynamical systems the variables involved relate to one another through a Cantor staircase function. When they are time variables, the staircases have well-known universal properties that suggest a connection with certain classical problems in Number Theory. In this paper we extend some of those universal properties to certain Cantor staircases that appear in Quantum Mechanics, where the variables involved are not time variables. We also develop some connections between the geometry of these Cantor staircases and the problem of approximating irrational numbers by rational ones, classical in Number Theory.
Registro:
| Documento: | Artículo |
| Título: | Cantor staircases in physics and diophantine approximations |
| Autor: | Piacquadio Losada, M.; Grynberg, S. |
| Filiación: | Departmento de Matemática, Fac. de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428-Buenos Aires, Argentina Departmento de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, 1063-Buenos Aires, Argentina |
| Año: | 1998 |
| Volumen: | 8 |
| Número: | 6 |
| Página de inicio: | 1095 |
| Página de fin: | 1106 |
| Título revista: | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
| Título revista abreviado: | Int. J. Bifurcation Chaos Appl. Sci. Eng. |
| ISSN: | 02181274 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada |
Referencias:
- Bak, P., The devil's staircase (1986) Phys. Today, pp. 38-45. , December
- Bruinsma, R., Bak, P., Self-similarity and fractal dimension of the devil's staircase in the one-dimensional ising model (1983) Phys. Rev., B27 (9), pp. 5924-5925
- Bumby, R., Hausdorff dimension of sets arising in number theory (1985) Lecture Notes in Mathematics, 1135, pp. 1-8. , Springer-Verlag, New York
- Cvitanovic, P., Jensen, M.H., Kadanoff, L.P., Procaccia, I., Renormalization, unstable manifolds and the fractal structure of mode-locking (1985) Phys. Rev. Lett., 55 (4), pp. 343-346
- Falconer, K., (1990) Fractal Geometry, 10, pp. 138-148. , John Wiley and Sons, Chichester-New York, Chap
- Grynberg, S., Piacquadio, M., Cantor Staircases in Physics and Higher Order Jarník Classes," in Preparation.
- Halsey, T., Jensen, M., Kadanoff, L., Procaccia, I., Shraiman, B., Fractal measures and their singularities: The characterization of strange sets (1987) Nucl. Phys. B, Proc. Suppl. 2, pp. 513-516
- Jensen, M.H., Multifractal scaling structure at the onset of chaos: Theory and experiment (1987) Nucl. Phys. B, Proc. Suppl. 2, pp. 487-496
Citas:
---------- APA ----------
Piacquadio Losada, M. & Grynberg, S. (1998) . Cantor staircases in physics and diophantine approximations. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 8(6), 1095-1106.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada [ ]
---------- CHICAGO ----------
Piacquadio Losada, M., Grynberg, S. "Cantor staircases in physics and diophantine approximations" . International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8, no. 6 (1998) : 1095-1106.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada [ ]
---------- MLA ----------
Piacquadio Losada, M., Grynberg, S. "Cantor staircases in physics and diophantine approximations" . International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 8, no. 6, 1998, pp. 1095-1106.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada [ ]
---------- VANCOUVER ----------
Piacquadio Losada, M., Grynberg, S. Cantor staircases in physics and diophantine approximations. Int. J. Bifurcation Chaos Appl. Sci. Eng. 1998;8(6):1095-1106.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada [ ]
