Communications in Mathematical Physics

, Volume 159, Issue 3, pp 433–441 | Cite as

On the distribution of zeros of a Ruelle zeta-function

  • A. Eremenko
  • G. Levin
  • M. Sodin


We study the limit distribution of zeros of a Ruelle χ-function for the dynamical systemz↦z2+c whenc is real andc→−2−0 and apply the results to the correlation functions of this dynamical system.


Neural Network Dynamical System Statistical Physic Correlation Function Complex System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Azarin, V.: On the asymptotic behavior of subharmonic functions of finite order. Math. USSR Sbornik36, 135 (1980)Google Scholar
  2. 2.
    Anderson, J., Baernstein, A.: The size of the set on which a meromorphic function is large. Proc. London Math. Soc.36, 518–539 (1978)Google Scholar
  3. 3.
    Beurling, A.: Some remarks on entire functions of exponential type. Collected Works, v.1, Boston: Birkhäuser 1989, p. 386Google Scholar
  4. 4.
    Brelot, M.: On topologies and boundaries in potential theory. Lect. Notes Math.175, Berlin, Heidelberg, New York: Springer 1971Google Scholar
  5. 5.
    Eremenko, A., Lyubich, M.: The dynamics of analytic transformations. Leningrad Math. J.1, 563–634 (1990)Google Scholar
  6. 6.
    Hardy, G.H.: On the zeroes of a class of integral functions. Mess. Math.34, 97–101 (1905); Collected Papers, v.IV, pp. 95–99Google Scholar
  7. 7.
    Hörmander, L.: The analysis of linear partial differential operators, Vol.1. Berlin, Heidelberg, New York: Springer 1983Google Scholar
  8. 8.
    Kadanoff, L., Tang, C.: Escape from strange repellers. Proc. Nat. Acad. Sci. USA81, 1276–1279 (1984)Google Scholar
  9. 9.
    Levin, G.: On Mayer's conjecture and zeros of entire functions. Preprint 17 (1991/92), Hebrew University, Jerusalem, 1992Google Scholar
  10. 10.
    Levin, G., Sodin, M., Yuditskii, P.: A Ruelle operator for a real Julia set. Commun. Math. Phys.141, 119–132 (1991)CrossRefGoogle Scholar
  11. 11.
    Levin, G., Sodin, M., Yuditskii, P.: Ruelle operators with rational weights for Julia sets. To appear in J. d' Analyse Math.Google Scholar
  12. 12.
    Ruelle, D.: Zeta-Functions for Expanding Maps and Anosov Flows. Invent. Math.34, 231–242 (1976)CrossRefGoogle Scholar
  13. 13.
    Ruelle, D.: Repellers for real analytic maps. Ergod. Th. & Dynam. Sys.2, 99–107 (1982)Google Scholar
  14. 14.
    Ruelle, D.: The thermodynamic formalism for expanding maps. Commun. Math. Phys.125, 239–262 (1989)CrossRefGoogle Scholar
  15. 15.
    Ruelle, D.: Spectral properties of a class of operators associated with conformal maps in two dimension. Commun. Math. Phys.144, 537–556 (1992)CrossRefGoogle Scholar
  16. 16.
    Sodin, M., Yuditskii, P.: The limit-periodic finite-difference operator onl 2(Z) associated with iterations of quadratic polynomials. J. Stat. Phys.60, 853–873 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • A. Eremenko
    • 1
  • G. Levin
    • 2
  • M. Sodin
    • 3
  1. 1.Purdue UniversityWest LafayetteUSA
  2. 2.Institute of MathematicsHebrew UniversityJerusalemIsrael
  3. 3.Institute of Low Temperature Physics and EngineeringKharkovUkraine

Personalised recommendations