Skip to main content
SpringerLink
Log in

Incommensurability of liouvillean dynamics and information dynamics

  • Conference paper
  • First Online:
Parallelism, Learning, Evolution (WOPPLOT 1989)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 565))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, Berlin, 1983)

    Google Scholar 

  2. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983)

    Google Scholar 

  3. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985)

    Google Scholar 

  4. R. Shaw, Z. Naturforsch. 36 a, 80 (1981)

    Google Scholar 

  5. J. D. Farmer, Z. Naturforsch. 37 a, 1304 (1982)

    Google Scholar 

  6. A. M. Fraser, Ph.D. thesis, University of Texas at Austin, 1988

    Google Scholar 

  7. C. E. Shannon and C. Weaver, The Mathematical Theory of Communication (Univ. of Illinois Press, 1962)

    Google Scholar 

  8. A. N. Kolmogorov, Dokl. Akad. Nauk. 98, 527 (1959)

    Google Scholar 

  9. J. B. Pesin, Russ. Math. Survey 32, 455 (1977) (Usp. Math. Nauk 32, 55 (1977))

    Google Scholar 

  10. H. Atmanspacher, Found. Phys. 19, 553 (1989)

    Google Scholar 

  11. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982)

    Google Scholar 

  12. F. Hausdorff, Math. Ann. 79, 157 (1919)

    Google Scholar 

  13. F. Takens, in Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898, eds. D. A. Rand and L. S. Young (Springer, Berlin, 1981), p.366

    Google Scholar 

  14. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980)

    Google Scholar 

  15. Among the pioneering publications are P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983); P. Grassberger and I. Procaccia, Phys. Rev. A 28, 2591 (1983); Y. Termonia and Z. Alexandrovitch, Phys. Rev. Lett. 45, 1265 (1983); R. Badii and A. Politi, J. Stat. Phys. 40, 725 (1985)

    Google Scholar 

  16. G. Mayer-Kress, ed., Dimensions and entropies in dynamical systems (Springer, Berlin, 1986)

    Google Scholar 

  17. A. Brandstater, J. Swift, H. L. Swinney, A. Wolf, J. D. Farmer, E. Jen, and P. J. Crutchfield, Phys. Rev. Lett. 51, 1441 (1983); J.-C. Roux, R. H. Simoyi, and H. L. Swinney, Physica 8 D, 257 (1983)

    Google Scholar 

  18. W. Lauterborn and J. Holzfuss, Phys. Lett. 115 A, 369 (1986)

    Google Scholar 

  19. A. Babloyantz, J. M. Salazar, and C. Nicolis, Phys. Lett. 111 A, 152 (1985)

    Google Scholar 

  20. G. Nicolis and C. Nicolis, Proc. Ntl. Acad. Sci. USA 83, 536 (1986)

    Google Scholar 

  21. A. M. Albano, J. Abounadi, T. H. Chyba, C. E. Searle, S. Yong, R. S. Gioggia, and N. B. Abraham, J. Opt. Soc. Am. B 2, 47 (1985); H. Atmanspacher and H. Scheingraber, Phys. Rev. A 34, 253 (1986)

    Google Scholar 

  22. M. Auvergne and A. Baglin, Astron. Astrophys. 168, 118 (1986); W. Voges, H. Atmanspacher, and H. Scheingraber, Ap. J. 320, 794 (1987)

    Google Scholar 

  23. H. Atmanspacher and H. Scheingraber, Found. Phys. 17, 939 (1987)

    Google Scholar 

  24. I. Prigogine, Non — Equilibrium Statistical Mechanics (Wiley, New York, 1962)

    Google Scholar 

  25. I. Prigogine, From Being to Becoming (Freeman, San Francisco, 1980)

    Google Scholar 

  26. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975)

    Google Scholar 

  27. G.M. Zaslavskii, Chaos in Dynamical Systems (Harwood, London, 1985) App.3

    Google Scholar 

  28. Y. Elkana, in Sciences and Cultures. Sociology of the Sciences, Vol.5, eds. E. Mendelsohn and Y. Elkana (Reidel, Dordrecht, 1981) pp. 1–76

    Google Scholar 

  29. P. Mittelstaedt, Sprache und Realität in der modernen Physik (BI Verlag, Mannheim, 1986.

    Google Scholar 

  30. G. Birkhoff, Lattice Theory, 3rd ed. (AMS Coll. Publ. Vol.25, Providence, Rhode Island, 1979)

    Google Scholar 

  31. M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974

    Google Scholar 

  32. G. Birkhoff and J. von Neumann, Ann. Math. 37, 823 (1936)

    Google Scholar 

  33. P. Lorenzen, Metamathematik (BI Verlag, Mannheim, 1962)

    Google Scholar 

  34. I. Prigogine and T. Petrofsky, Physica 147 A, 33, 439, 461 (1987)

    Google Scholar 

  35. P. Watzlawick, ed., Die erfundene Wirklichkeit (Piper, München, 1981)

    Google Scholar 

  36. F. Krueger, Physik und Evolution (Parey, Berlin, 1984); Theorie der Emergenz (unpublished manuscript, 1988)

    Google Scholar 

  37. K. Popper, The Logic of Scientific Discovery (Hutchinson, London, 1959)

    Google Scholar 

  38. P. Ablay, this volume

    Google Scholar 

  39. D. Finkelstein, Finite Physics (preprint, 1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Physik und Astrophysik, D-8046, Garching, FRG

    H. Atmanspacher

Authors
  1. H. Atmanspacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. D. Becker I. Eisele F. W. Mündemann

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Atmanspacher, H. (1991). Incommensurability of liouvillean dynamics and information dynamics. In: Becker, J.D., Eisele, I., Mündemann, F.W. (eds) Parallelism, Learning, Evolution. WOPPLOT 1989. Lecture Notes in Computer Science, vol 565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55027-5_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-55027-5_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55027-3

  • Online ISBN: 978-3-540-46663-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation