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Theoretical properties of fractal dimensions for fractal structures
1. | University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, Coronel López Peña Street, w/n, 30720 Santiago de la Ribera, Murcia, Spain |
References:
[1] |
F. G. Arenas and M. A. Sánchez-Granero, A characterization of non-archimedeanly quasimetrizable spaces, Rend. Istit. Mat. Univ. Trieste Suppl., 30 (1999), 21-30. |
[2] |
F. G. Arenas and M. A. Sánchez-Granero, A new approach to metrization, Topology Appl., 123 (2002), 15-26.
doi: 10.1016/S0166-8641(01)00165-1. |
[3] |
F. G. Arenas and M. A. Sánchez-Granero, A new metrization theorem, Boll. Unione Mat. Ital. (8), 5 (2002), 109-122. |
[4] |
F. G. Arenas and M. A. Sańchez-Granero, A characterization of self-similar symbolic spaces, Mediterr. J. Math., 9 (2012), 709-728.
doi: 10.1007/s00009-011-0146-4. |
[5] |
A. S. Besicovitch, Sets of fractional dimensions IV: On rational approximation to real numbers, J. Lond. Math. Soc., 9 (1934), 126-131.
doi: 10.1112/jlms/s1-9.2.126. |
[6] |
A. S. Besicovitch and H. D. Ursell, Sets of fractional dimensions V: On dimensional numbers of some continuous curves, J. Lond. Math. Soc., 12 (1937), 18-25.
doi: 10.1112/jlms/s1-12.45.18. |
[7] |
C. Brown and L. Liebovitch, Fractal Analysis, in: Series 07-165: Quantitative Applications in the Social Sciences, First ed., SAGE Publications Inc., New York, 2010. |
[8] |
C. Carathéodory, Über das lineare mass von punktmengen-eine verallgemeinerung das längenbegriffs, Nach. Ges. Wiss. Göttingen, (1914), 406-426. |
[9] |
K. Falconer, Fractal Geometry. Mathematical Foundations and Applications, John Wiley & Sons, Chichester, 1990. |
[10] |
K. Falconer, Fractal Geometry. Mathematical Foundations and Applications, Third Edition, John Wiley & Sons, Chichester, 2014. |
[11] |
J. Feder, Fractals, Plenum Press, New York, 1988.
doi: 10.1007/978-1-4899-2124-6. |
[12] |
M. Fernández-Martínez and M. A. Sánchez-Granero, Fractal dimension for fractal structures, Topology Appl., 163 (2014), 93-111.
doi: 10.1016/j.topol.2013.10.010. |
[13] |
M. Fernández-Martínez and M. A. Sánchez-Granero, Fractal dimension for fractal structures: A Hausdorff approach, Topology Appl., 159 (2012), 1825-1837.
doi: 10.1016/j.topol.2011.04.023. |
[14] |
M. Fernández-Martínez, M. A. Sánchez-Granero and J. E. Trinidad Segovia, Fractal dimension for fractal structures: Applications to the domain of words, Appl. Math. Comput., 219 (2012), 1193-1199.
doi: 10.1016/j.amc.2012.07.029. |
[15] |
M. Fernández-Martínez, M. A. Sánchez-Granero and J. E. Trinidad Segovia, Fractal Dimensions for Fractal Structures and Their Applications to Financial Markets, Aracne, Roma, 2013. |
[16] |
M. Fernández-Martínez and M. A. Sánchez-Granero, Fractal dimension for fractal structures: A Hausdorff approach revisited, Journal of Mathematical Analysis and Applications, 409 (2014), 321-330.
doi: 10.1016/j.jmaa.2013.07.011. |
[17] |
M. Fernández-Martínez and M. A. Sánchez-Granero, How to calculate the Hausdorff dimension using fractal structures, Appl. Math. Comput., 264 (2015), 116-131.
doi: 10.1016/j.amc.2015.04.059. |
[18] |
F. Hausdorff, Dimension und äusseres mass, Math. Ann., 79 (1919), 157-179. |
[19] |
L. Pontrjagin and L. Schnirelman, Sur une proprieté métrique de la dimension, Ann. Math., 33 (1932), 156-162.
doi: 10.2307/1968109. |
[20] |
M. A. Sánchez-Granero, Fractal structures, in Asymmetric Topology and its Applications, Quaderni di Matematica, 26, Seconda Univ. Napoli, Caserta, 2011, 211-245. |
show all references
References:
[1] |
F. G. Arenas and M. A. Sánchez-Granero, A characterization of non-archimedeanly quasimetrizable spaces, Rend. Istit. Mat. Univ. Trieste Suppl., 30 (1999), 21-30. |
[2] |
F. G. Arenas and M. A. Sánchez-Granero, A new approach to metrization, Topology Appl., 123 (2002), 15-26.
doi: 10.1016/S0166-8641(01)00165-1. |
[3] |
F. G. Arenas and M. A. Sánchez-Granero, A new metrization theorem, Boll. Unione Mat. Ital. (8), 5 (2002), 109-122. |
[4] |
F. G. Arenas and M. A. Sańchez-Granero, A characterization of self-similar symbolic spaces, Mediterr. J. Math., 9 (2012), 709-728.
doi: 10.1007/s00009-011-0146-4. |
[5] |
A. S. Besicovitch, Sets of fractional dimensions IV: On rational approximation to real numbers, J. Lond. Math. Soc., 9 (1934), 126-131.
doi: 10.1112/jlms/s1-9.2.126. |
[6] |
A. S. Besicovitch and H. D. Ursell, Sets of fractional dimensions V: On dimensional numbers of some continuous curves, J. Lond. Math. Soc., 12 (1937), 18-25.
doi: 10.1112/jlms/s1-12.45.18. |
[7] |
C. Brown and L. Liebovitch, Fractal Analysis, in: Series 07-165: Quantitative Applications in the Social Sciences, First ed., SAGE Publications Inc., New York, 2010. |
[8] |
C. Carathéodory, Über das lineare mass von punktmengen-eine verallgemeinerung das längenbegriffs, Nach. Ges. Wiss. Göttingen, (1914), 406-426. |
[9] |
K. Falconer, Fractal Geometry. Mathematical Foundations and Applications, John Wiley & Sons, Chichester, 1990. |
[10] |
K. Falconer, Fractal Geometry. Mathematical Foundations and Applications, Third Edition, John Wiley & Sons, Chichester, 2014. |
[11] |
J. Feder, Fractals, Plenum Press, New York, 1988.
doi: 10.1007/978-1-4899-2124-6. |
[12] |
M. Fernández-Martínez and M. A. Sánchez-Granero, Fractal dimension for fractal structures, Topology Appl., 163 (2014), 93-111.
doi: 10.1016/j.topol.2013.10.010. |
[13] |
M. Fernández-Martínez and M. A. Sánchez-Granero, Fractal dimension for fractal structures: A Hausdorff approach, Topology Appl., 159 (2012), 1825-1837.
doi: 10.1016/j.topol.2011.04.023. |
[14] |
M. Fernández-Martínez, M. A. Sánchez-Granero and J. E. Trinidad Segovia, Fractal dimension for fractal structures: Applications to the domain of words, Appl. Math. Comput., 219 (2012), 1193-1199.
doi: 10.1016/j.amc.2012.07.029. |
[15] |
M. Fernández-Martínez, M. A. Sánchez-Granero and J. E. Trinidad Segovia, Fractal Dimensions for Fractal Structures and Their Applications to Financial Markets, Aracne, Roma, 2013. |
[16] |
M. Fernández-Martínez and M. A. Sánchez-Granero, Fractal dimension for fractal structures: A Hausdorff approach revisited, Journal of Mathematical Analysis and Applications, 409 (2014), 321-330.
doi: 10.1016/j.jmaa.2013.07.011. |
[17] |
M. Fernández-Martínez and M. A. Sánchez-Granero, How to calculate the Hausdorff dimension using fractal structures, Appl. Math. Comput., 264 (2015), 116-131.
doi: 10.1016/j.amc.2015.04.059. |
[18] |
F. Hausdorff, Dimension und äusseres mass, Math. Ann., 79 (1919), 157-179. |
[19] |
L. Pontrjagin and L. Schnirelman, Sur une proprieté métrique de la dimension, Ann. Math., 33 (1932), 156-162.
doi: 10.2307/1968109. |
[20] |
M. A. Sánchez-Granero, Fractal structures, in Asymmetric Topology and its Applications, Quaderni di Matematica, 26, Seconda Univ. Napoli, Caserta, 2011, 211-245. |
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