Advertisement

Fractal Aspects of Galaxy Clustering

  • Vicent J. Martínez
Chapter
Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 3)

Abstract

In the past decade, the mathematical concept of fractal has exerted a great influence in a large variety of scientific disciplines. It is very common to find recent papers on the application of fractals to different fields in Physics, Chemistry, Biology, etc. The success of the fractal geometry in the description of many systems is due to the fact that deep insights into very simple objects show how fractal measures are more natural for their study.

Keywords

Fractal Dimension Minimal Span Tree Correlation Dimension Hausdorff Dimension Galaxy Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Argoul, F., Arneodo, A., Elezgaray, J., Grasseau, G., Murenzi, R. (1989): Phys. Lett. A 135, 327.CrossRefADSMathSciNetGoogle Scholar
  2. Arneodo, A., Grasseau, G., Holschneider, M. (1988): Phys. Rev. Lett. 61, 2281.CrossRefADSMathSciNetGoogle Scholar
  3. Atmanspacher, H., Scheingraber, H., Wiedenmann, G. (1989): Phys. Rev. A 40i, 3954.CrossRefADSGoogle Scholar
  4. Bardeen, J.M., Bond, J.R., Kaiser, N., Szalay, A.S. (1986): Astrophys. J. 304, 15.CrossRefADSGoogle Scholar
  5. Barnsley M. (1988): Fractals Everywhere, (Academic Press, San Diego).zbMATHGoogle Scholar
  6. Bhavsar, S.P., Ling, N. (1988): Astrophys. J. Letters 331, L63.CrossRefADSGoogle Scholar
  7. Bonometto, S.A., and Sharp, N.A. (1980): Astron. Astrophys. 92, 222.ADSGoogle Scholar
  8. Broadhurst, T.J., Ellis, R.S., Koo, D.C., Szalay, A.S. (1990): Nature 343, 726.CrossRefADSGoogle Scholar
  9. Buchert, T. (1989a): Rev. Mod. Astr. 2, 267.ADSGoogle Scholar
  10. Buchert, T. (1989b): Astron. Astrophys. 223, 9.ADSMathSciNetGoogle Scholar
  11. Buchert, T., Mo, H. (1990): Astron. Astrophys., in press.Google Scholar
  12. Buchert, T. (1991): in Physical Cosmology, (Frontières, Paris), in press.Google Scholar
  13. Buchert, T., Martínez, V.J. (1991): in preparation.Google Scholar
  14. Calzetti, D., Giavalisco, M., Ruffini, R. (1988): Astron. Astrophys. 198, 1.zbMATHADSMathSciNetGoogle Scholar
  15. Castagnoli, C, Provenzale, A. (1991): Astron. Astrophys., in press.Google Scholar
  16. Charlier, C.V.L. (1922): Ark. Math. Astr. Fys. 16, 1.Google Scholar
  17. Coleman P.H., Pietronero, L., Sanders R.H. (1988): Astron. Astrophys. 200, L32.ADSGoogle Scholar
  18. Combes, J.M., Grossman, A., Tchamitchian, P. (Eds.) (1988): Wavelets (Springer-Verlag, Berlin).Google Scholar
  19. Davis, M., Huchra, J. (1982): Astron. J. 254, 437.ADSGoogle Scholar
  20. Davis, M., Peebles, P.J.E. (1983): Astrophys. J. 267 465.CrossRefADSGoogle Scholar
  21. Davis, M., Meiskin, A., Strauss, M. A., da Costa, L. N., Yahil, A. (1988): Astrophys. J. 333, L9.CrossRefADSGoogle Scholar
  22. de Lapparent, V., Geller, M.J., Huchra, J.P. (1986): Astrophys. J. Letters 302, L1.CrossRefADSGoogle Scholar
  23. de Lapparent, V., Geller, M.J., Huchra, J.P. (1988): Astrophys. J. 332, 44.CrossRefADSGoogle Scholar
  24. de Lapparent, V., Geller, M.J., Huchra, J.P. (1990): preprint.Google Scholar
  25. de Vaucouleurs, G. (1970): Science 167, 1203.CrossRefADSGoogle Scholar
  26. Domínguez-Tenreiro, R., Martínez, V.J. (1989): Astrophys. J. Letters 339, L9.CrossRefADSGoogle Scholar
  27. Domínguez-Tenreiro, R., Roy, L. J., Martínez, V.J. (1990): preprint.Google Scholar
  28. Efstathiou, G., Fall, S.M., Hogan, G. (1979): Monthly Not. Roy. Astron. Soc. 189,203.ADSGoogle Scholar
  29. Einasto, J., Klypin, A.A., Saar, E., Shandarin, S.F. (1984): Monthly Not. Roy. Astron. Soc. 206, 529.ADSGoogle Scholar
  30. Einasto, J., Klypin, A.A., Saar, E. (1986): Monthly Not. Roy. Astron. Soc. 219, 457.ADSGoogle Scholar
  31. Falconer, K.J. (1985): The Geometry of Fractal Sets, (Cambridge Univ. Préss, Cambridge).zbMATHCrossRefGoogle Scholar
  32. Feder, J. (1988): Fractals, (Plenum Press, New York).zbMATHGoogle Scholar
  33. Fournier d’Albe, E. E. (1907): Two New Worlds, (Longmans Green, London).Google Scholar
  34. Frisch, U., Parisi, G. (1985): in Turbulence and Predictability of Geophysical Flows and Climatic Dynamics, Eds. N. Ghil and R. Benzi, (North Holland, Amsterdam).Google Scholar
  35. Geller, M.J., Huchra J.P. (1989): Science 246, 897.CrossRefADSGoogle Scholar
  36. Gill, A.G., Henriksen, R.N. (1990): preprint.Google Scholar
  37. Giovanelli, R., Haynes, M.P., Chincarini, G.L. (1986): Astrophys. J. 300, 77.CrossRefADSGoogle Scholar
  38. Grassberger, P., Procaccia, I. (1983): Phys. Rev. Lett. 50, 346.CrossRefADSMathSciNetGoogle Scholar
  39. Grassberger P., Badii R., Politi, A. (1988): J. Stat. Phys. 51, 135.zbMATHCrossRefADSMathSciNetGoogle Scholar
  40. Groth, E.J., Peebles, P.J.E. (1977): Astrophys. J. 217, 385.CrossRefADSGoogle Scholar
  41. Halsey, T.C., Jensen, M.H., Kadanoff, L.P., Procaccia, I., Shraiman, B.I. (1986): Phys. Rev. A. 33, 1141.CrossRefADSMathSciNetzbMATHGoogle Scholar
  42. Hamilton, A.J.S (1988): Astrophys. J. Letters 331, L59.CrossRefADSGoogle Scholar
  43. Hausdorff, F. (1919): Math. Ann. 79, 157.CrossRefMathSciNetGoogle Scholar
  44. Hentschel, H.G.E., Procaccia, I. (1983): Physica 8D, 435.ADSMathSciNetGoogle Scholar
  45. Huchra, J.P., Davis, M., Latham, D., Tonry, J. (1983): Astrophys. J. Suppl. 52, 89.CrossRefADSGoogle Scholar
  46. Huchra, J., Geller, M.J., de Lapparent, V, Corwin, H. (1990): Astrophys. J. Suppl. 72, 433.CrossRefADSGoogle Scholar
  47. Jones, B.J.T., Martínez, V.J., Saar, E., Einasto, J. (1988): Astrophys. J. Letters 332, L1.CrossRefADSGoogle Scholar
  48. Kirshner, R.P., Oemler, A., Schechter, P.L., Shectman, S.A. (1981): Astrophys. J. Letters 248, L57.CrossRefADSGoogle Scholar
  49. Kirshner, R.P., Oemler, A., Schechter, P.L., Shectman, S.A. (1987): Astrophys. J. 314, 493.CrossRefADSGoogle Scholar
  50. Klypin, A.A., Einasto, J., Einasto, M., Saar, E. (1989): Monthly Not. Roy. Astron. Soc. 237, 929.ADSGoogle Scholar
  51. Kolmogorov, A. N., Tihomirov, V. M. (1959): Upekhi Matematicheskikh Navk 14, 3.zbMATHMathSciNetGoogle Scholar
  52. Lifshitz, E. M. (1946): J. Phys. 5, 84.Google Scholar
  53. Mandelbrot, B.B. (1974): J. Fluid. Mech. 62, 331.zbMATHCrossRefADSGoogle Scholar
  54. Mandelbrot, B.B. (1975): C.R. Acad. Sc. Paris A 105, 1551.ADSMathSciNetGoogle Scholar
  55. Mandelbrot, B.B. (1977): Fractals: Form, Chance and Dimension (Freeman, San Francisco).zbMATHGoogle Scholar
  56. Mandelbrot, B.B. (1982): The Fractal Geometry of Nature (Freeman, San Francisco).zbMATHGoogle Scholar
  57. Mandelbrot, B.B. (1989): in Large Scale-Structure and Motions in the Universe, Eds. M. Mezzeti, G. Giuricin, F. Mardirossian, M. Ramella, (Kluwer Acad. Publ., Dordrecht), p. 259.Google Scholar
  58. Martínez, V.J. (1990): in Fractals in Astronomy, Ed. A. Heck, Vistas Astron. 33, 337Google Scholar
  59. Martínez, V.J., Jones, B.J.T. (1990): Monthly Not. Roy. Astron. Soc. 242, 517.ADSGoogle Scholar
  60. Martínez, V.J., Jones, B.J.T., Domínguez-Tenreiro, R., van de Weygaert, R. (1990): Astrophys. J. 357, 50.CrossRefADSGoogle Scholar
  61. Martínez, V.J., Portilla, M., Jones, B.J.T. (1991): in preparation.Google Scholar
  62. Martínez, V.J., Saar, E. (1991): in preparation.Google Scholar
  63. Maurogordato, S., Lachièze-Rey, M. (1987): Astrophys. J. 320, 13.CrossRefADSGoogle Scholar
  64. Maurogordato, S., Lachièze-Rey, M. (1990): preprint.Google Scholar
  65. Meakin, P. (1987): Phys. Rev. A 36, 2833.CrossRefADSGoogle Scholar
  66. Paladin, G., Vulpiani, A. (1987): Phys. Repts. 156, 147.CrossRefADSMathSciNetGoogle Scholar
  67. Peebles, P.J.E. (1980): The Large-Scale Structure of the Universe (Princeton Univ. Press, Princeton).Google Scholar
  68. Peebles, P.J.E. (1989): in Cosmology and Particle Physics, Eds. J.F Nieves, D.R. Altschuler (World Scientific, Singapore).Google Scholar
  69. Pietronero, L., Tossati, E. (Eds.), 1986, Fractals in Physics. (North Holland, Amsteredam).Google Scholar
  70. Pietronero, L. (1987): Physica A 144, 257.zbMATHCrossRefADSGoogle Scholar
  71. Rényi, A. (1970): Probability Theory (North Holland, Amsterdam).Google Scholar
  72. Rivolo, A.R. (1986): Astrophys. J. 301, 70.CrossRefADSGoogle Scholar
  73. Saar, E. (1989): Proc. 11th Krakow School of Cosmology, Eds. H. Durbeck, P. Flin (Springer-Verlag, Berlin).Google Scholar
  74. Saar, E., Saar, V. (1990): preprint.Google Scholar
  75. Schechter, P. (1976): Astrophys. J. 203, 297.CrossRefADSGoogle Scholar
  76. Shane, C.D., Wirtanen, C.A. (1967): Publ. Lick Obs. 22, part 1.Google Scholar
  77. Slezak, E., Bijaoui, A., Maars, G. (1990): Astron. Astrophys. 227, 301.ADSGoogle Scholar
  78. Soneira, R., Peebles, P.J.E. (1978): Astron. J. 83, 845.CrossRefADSGoogle Scholar
  79. Stanley, H.E., Meakin, P. (1988): Nature 335, 405.CrossRefADSGoogle Scholar
  80. Takayasu, H. (1989): Fractals in the Physical Sciences (Manchester Univ. Press, Manchester).Google Scholar
  81. Tully R.B., Fisher J.R. (1978): in The Large-Scale Structure of the Universe, Eds. M.S. Longair, J. Einasto (Reidel Publ. Co., Dordrecht), p 214.Google Scholar
  82. Upton G.J.G., Fingleton, B. (1987): Spatial Data Analysis by Example, Vol. 1 (Wiley, New York).Google Scholar
  83. Van de Weygaert, R., Jones, B.J.T., Martínez, V. J. (1990): preprint.Google Scholar
  84. White, S.D.M., Davis, M., Efstathiou, G., Frenk, C.S. (1987): Nature 330, 451.CrossRefADSGoogle Scholar
  85. Zel’dovich, Ya.B. (1970): Astron. Astrophys. 5, 84.ADSGoogle Scholar
  86. Zel’dovich, Ya.B. (1972): Monthly Not. Roy. Astron. Soc. 160, 1P.ADSGoogle Scholar
  87. Zel’dovich, Ya.B. (1978): in The Large-Scale Structure of the Universe, edd. M.S. Longair, J. Einasto (Reidel Publ. Co., Dordrecht), p. 409.Google Scholar
  88. Zwicky, F., Herzog, E., Wild, P., Karpowicz, M., Kowal, C.T. (1961–1968): Catalogue of Galaxies and Clusters of Galaxies (California Inst. Techn., Pasadena), Vol 1–6.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Vicent J. Martínez
    • 1
  1. 1.Departament de Matemàtica Aplicada i AstronomiaUniversitat de ValènciaBurjassotSpain

Personalised recommendations