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Linear response in chaotic states of discrete dynamics

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Zeitschrift für Physik B Condensed Matter

Abstract

The importance of the coupling operatorA of an external disturbance to a 1-dimensional map is discussed. A time dependent susceptibility χ BA t is introduced describing the linear response in chaotic states observed with observableB. Its properties are given, its temporal decay, and its relation to correlations (fluctuations). Some examples are evaluated explicitely. The static susceptibility depends on the correlation decay as usual, and diverges if the state changes its character under the perturbation.

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References

  1. Heldstab, J., Thomas, H., Geisel, T., Radons, G.: Z. Phys. B-Condensed Matter50, 141 (1983)

    Google Scholar 

  2. Geisel, T., Heldstab, J., Thomas, H.: Z. Phys. B-Condensed Matter 55, 165 (1984)

    Google Scholar 

  3. Giglio, M., Musazzi, S., Perini, U.: Phys. Rev. Lett.47, 243 (1981)

    Google Scholar 

  4. Horner, H.: Phys. Rev.27, 1270 (1983)

    Google Scholar 

  5. Mathematical monographs for example Gumowski, I., Mira, C.: Recurrences and Discrete Dynamic Systems. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  6. Targonski, G.: Topics in Iteration Theory. Göttingen, Zürich: Vandenhoek and Ruprecht 1981

    Google Scholar 

  7. Physical aspects Grossmann, S.: In: Evolution of Chaos and Order. Haken H. (ed.). Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  8. Grossmann, S.: In: Non-Equilibrium Cooperative Phenomena in Physics and Related Fields. Velarde, M.G. (ed.). ASI-Series. New York, London: Plenum Press 1984

    Google Scholar 

  9. Geisel, T., Nierwetberg, J.: Phys. Rev. Lett.48, 7 (1982)

    Google Scholar 

  10. Grossmann, S., Fujisaka, H.: Phys. Rev. A26, 1779 (1982)

    Google Scholar 

  11. Schell, M., Fraser, S., Kapral, R.: Phys. Rev. A26, 504 (1982)

    Google Scholar 

  12. Györgyi, G., Szépfalusy, P.: J. Stat. Phys.34, 451 (1984)

    Google Scholar 

  13. Misiurewicz, M.: Absolutely continuous measures for certain maps of an interval. Publ. Math. IHES 1979

  14. I think the reader can easily distinguish the two differen δ's, one appearing in the δ-distribution (2) and the other in the disturbance δf(y, t) or δp *

  15. Grossmann, S., Thomae, S.: Z. Naturforsch.32a, 1353 (1977)

    Google Scholar 

  16. Thomae, S., Grossmann, S.: J. Stat. Phys.26, 485 (1981)

    Google Scholar 

  17. Hemmer, P.C.: J. Phys. Math. Gen.17, L247 (1984)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Fachbereich Physik der Philipps-Universität Marburg, Renthof 6, D-3550, Marburg, Germany

    S. Grossmann

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  1. S. Grossmann
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Grossmann, S. Linear response in chaotic states of discrete dynamics. Z. Physik B - Condensed Matter 57, 77–84 (1984). https://doi.org/10.1007/BF01679929

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  • DOI: https://doi.org/10.1007/BF01679929

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