Measures of Dimensions from Astrophysical Data

  • H. Atmanspacher
  • V. Demmel
  • G. Morfill
  • H. Scheingraber
  • W. Voges
  • G. Wiedenmann
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

The complexity of a system may have numerous aspects, and the problems to define complexity in a generally relevant manner seem to increase self-similarly with the intensity of corresponding efforts. In this sense it is certainly a complex task to provide a compulsory concept of the notion of complexity. In the present contribution we deal with dimensions as measures of complexity. Mathematically the concept of dimensions reflects the scaling properties of point distributions on a given support. Speaking in terms of physical systems, this support is usually a vector space. Studying the structural properties of a system refers simply to structures in position space, whereas functional properties of a system are related to the structure of its dynamics in phase space.

Keywords

Neutron Star Compact Object Rayleigh Taylor Instability Boundary Correction Mass Accretion Rate 
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. 1.
    J. R. Buchler, J. M. Perdang, and E. A. Spiegel, eds., Chaos in Astrophysics, ( Reidel, Dordrecht, 1985 )Google Scholar
  2. 2.
    H. Ogelman and E. P. J. van den Heuvel, eds., Timing Neutron Stars ( Kluwer, Dordrecht, 1989 )Google Scholar
  3. 3.
    G. Hasinger and M. van der Klis, Astron. Astrophys. 225, 79 (1989)Google Scholar
  4. 4.
    P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)MathSciNetCrossRefGoogle Scholar
  5. 5.
    W. Voges, H. Atmanspacher, and H. Scheingraber, Ap. J. 320, 794 (1987)CrossRefGoogle Scholar
  6. 6.
    H. Atmanspacher, H. Scheingraber, and W. Voges, Phys. Rev. A 37, 1314 (1988)CrossRefGoogle Scholar
  7. 7.
    H. Atmanspacher, H. Scheingraber, and W. Voges: Timing Neutron Stars, eds. H. Ogelman and E. P. J. van den Heuvel ( Kluwer, Dordrecht, 1989 ) p. 219Google Scholar
  8. 8.
    H. Atmanspacher, H. Scheingraber, and W. Voges: Data Analysis in Astronomy III, eds. V. di Gesu and L. Scarsi ( Plenum Press, New York, 1989 )Google Scholar
  9. 9.
    W. Voges, H. Atmanspacher, and H. Scheingraber, Adv. Space Res. 8 (2)497 (1988)CrossRefGoogle Scholar
  10. 10.
    G. E. Morfill, H. Atmanspacher, V. Demmel, H. Scheingraber, and W. Voges: Timing Neutron Stars, eds. H. Ogelman and E. P. J. van den Heuvel ( Kluwer, Dordrecht, 1989 ) p. 71Google Scholar
  11. 11.
    N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980)CrossRefGoogle Scholar
  12. 12.
    F. Takens, in Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898, eds. D. A. Rand and L. S. Young ( Springer, Berlin, 1981 ), p. 366Google Scholar
  13. 13.
    J. P. Norris and T. A. Matilsky, Ap. J. 346, 912 (1989)CrossRefGoogle Scholar
  14. 14.
    P. Grassberger and I. Procaccia, Phys. Rev. A 28, 2591 (1983)Google Scholar
  15. 15.
    K. Pawelzik and H. G. Schuster, Phys. Rev. A 35, 481 (1987)Google Scholar
  16. 16.
    T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Phys. Rev. A 33, 1141 (1986)MathSciNetGoogle Scholar
  17. 17.
    J. Feder, Fractals (Plenum, New York, 1988) Chap. 6. 4MATHGoogle Scholar
  18. 18.
    E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963)CrossRefGoogle Scholar
  19. 19.
    H. Atmanspacher and H. Scheingraber, Phys. Rev. A 34, 253 (1986)Google Scholar
  20. 20.
    H. Atmanspacher, H. Scheingraber, and V. M. Baev, Phys. Rev. A 35, 142 (1987)Google Scholar
  21. 21.
    Yu. M. Ajvasjan, V. V. Ivanov, S. A. Kovalenko, V. M. Baev, E. A. Sviridenkov, H. Atmanspacher, and H. Scheingraber, Appl. Phys. B 46, 175 (1988)Google Scholar
  22. 22.
    G. E. Morfill, V. Demmel, and H. Atmanspacher, Mitt. Astron. Ges. 68, 251 (1987)Google Scholar
  23. 23.
    V. Demmel, G.E. Morfill, and H. Atmanspacher, in: Timing Neutron Stars, eds. H. Ógelman and E. P. J. van den Heuvel ( Kluwer, Dordrecht, 1989 ) p. 749Google Scholar
  24. 24.
    V. Demmel, H. Atmanspacher, and G. Morfill, Adv. Space Res. 8, (2)583 (1988)CrossRefGoogle Scholar
  25. 25.
    V. Demmel, diploma thesis, 1987Google Scholar
  26. 26.
    H. Doll and W. Brinkmann, Astron. Astrophys. 173, 86 (1986)Google Scholar
  27. 27.
    Y.-M. Wang, M. Nepveu, and J. A. Robertson, Ap. J. 135, 66 (1984)Google Scholar
  28. 28.
    A. A. Penzias and R. W. Wilson, Ap. J. 142, 419 (1965)CrossRefGoogle Scholar
  29. 29.
    F.Zwicky, E. Herzog, P. Wild, M. Karpowicz, and C. T. Kowal, Catalogue of Galaxies and Clusters of Galaxies, Vols.1–6 (California Institute of Technology, Pasadena, 1962–68)Google Scholar
  30. 30.
    C. D. Shane and C. A. Wirtanen, Proc. Amer. Phil. Soc. 94, 13 (1950)Google Scholar
  31. 31.
    K. Rudnicki, T. Z. Dworak, P. Flin, B. Baranowski, and A. Sendranowski, Acta Cosmologica 1, 7 (1973)Google Scholar
  32. 32.
    J. P. Huchra, M. Davis, D. Latham, and J. Tonry, Ap. J. Suppl. 52, 89 (1983)CrossRefGoogle Scholar
  33. 33.
    J. P. Huchra, V. de Lapparent, M.J. Geller, M.J. Kurtz, E. Horine, J. Peters, and S. Tokarz, 1989, to be publishedGoogle Scholar
  34. 34.
    L. Pietronero, Physica 144 A, 257 (1987)Google Scholar
  35. 35.
    G. Wiedenmann and H. Atmanspacher, Astron. Astrophys. 229, 283 (1990)Google Scholar
  36. 36.
    B. B. Mandelbrot, Fractals and Multifractals: Noise, Turbulence, and Galaxies ( Springer, New York, 1989 )Google Scholar
  37. 37.
    V. de Lapparent, M. J. Geller, and J. P. Huchra, Ap. J. 322, 44 (1988)CrossRefGoogle Scholar
  38. 38.
    M. Davis, A. Meiksin, M. A. Strauss, L. N. da Costa, and A. Yahil, Ap. J. (Letters) 333, L9 (1988)CrossRefGoogle Scholar
  39. 39.
    B. B. Mandelbrot, The Fractal Geometry of Nature ( Freeman, San Francisco, 1982 )MATHGoogle Scholar
  40. 40.
    P. J. E Peebles, The Large-Scale Structure of the Universe (Princeton University Press, 1980 )Google Scholar
  41. 41.
    P. J. E. Peebles and M. G. Hauser, Ap. J. Suppl. 28, 19 (1974)CrossRefGoogle Scholar
  42. 42.
    P. H. Coleman, L. Pietronero, and R. H. Sanders, Astron. Astrophys. 200, L32 (1988)Google Scholar
  43. 43.
    P. Grassberger, R. Badii, and A. Politi, J. Stat. Phys. 51, 135 (1988)MathSciNetMATHCrossRefGoogle Scholar
  44. 44.
    H. Atmanspacher, H. Scheingraber, and G. Wiedenmann, Phys. Rev. A 40, 3954 (1989)Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • H. Atmanspacher
    • 1
  • V. Demmel
    • 1
  • G. Morfill
    • 1
  • H. Scheingraber
    • 1
  • W. Voges
    • 1
  • G. Wiedenmann
    • 1
  1. 1.Max-Planck-Institut für extraterrestrische PhysikGarchingGermany

Personalised recommendations