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On Mayer's conjecture and zeros of entire functions

Published online by Cambridge University Press:  19 September 2008

G. Levin
G. Levin
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel
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Abstract

We study the spectrum of a transfer operator that gives a counterexample to the conjecture of Mayer. The effect of perturbations is considered.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 3 , September 1994 , pp. 565 - 574
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

[I]Beardon, A.. Iteration of Rational Functions. Springer: Berlin, 1991.CrossRefGoogle Scholar
[2]Douady, A. and Hubbard, J.H.. Iteration des polynomes quadratiques complexes. CR Acad. Sci. Paris. 294 (1982), 123–126.Google Scholar
[3]Denker, M. and Urbanski, M.. Ergodic theory of equilibrium states for rational maps. Nonlinearity 4 (1991), 103–134.CrossRefGoogle Scholar
[4]Fried, D.. The zeta functions of Ruelle and Selberg I. Ann. Sci. E. N.S. 19 (1986), 491–517.Google Scholar
[5]Hardy, G.H.. On the zeroes of a class of integral functions. Messengerof Mathematics 34 (1905), 97–101.Google Scholar
[6]Levin, B. Ya. Distribution of Zeros of Entire Functions. American Mathematical Society: Providence, RI, 1964.CrossRefGoogle Scholar
[7]Levin, G., Sodin, M. and Yuditskii, P.. A Ruelle operator for a real Julia set. Commun. Math. Phys. 141 (1991), 119–132.CrossRefGoogle Scholar
[8]Levin, G., Sodin, M. and Yuditskii, P.. Ruelle operators with rational weights for Julia sets. J. d'Analyse Math. To appear.Google Scholar
[9]Mayer, D.H.. On the location of poles of Ruelle's zeta function for Gauss' map. Dynamical Systems and Ergodic Theory. Vol. 23. Banach Center Publications: Warsaw, 1989. pp. 101–111.Google Scholar
[10]Przytycki, F.. On the Perron-Frobenius-Ruelle operator for rational maps on the Riemann sphere and for Holder continuous functions. Bol. Soc. Bras. Mat. 20 (1990), 95–125.CrossRefGoogle Scholar
[II]Ruelle, D.. Zeta-functions for expanding maps and Anosov flows. Invent. Math. 34 (1976), 231–242.CrossRefGoogle Scholar
[12]Ruelle, D.. Thermodynamic Formalism. Addison-Wesley: New York, 1978.Google Scholar
[13]Ruelle, D.. Repellers for real analytic maps. Ergod. Th. & Dynam. Sys. 2 (1982), 99–107.CrossRefGoogle Scholar
[14]Ruelle, D.. The termodynamic formalism for expanding maps. Commun. Math. Phys. 125 (1989), 239–262.CrossRefGoogle Scholar
[15]Ruelle, D.. Spectral properties of a class of operators associated with conformal maps in two dimensions. Commun. Math. Phys. 144 (1992), 537–556.CrossRefGoogle Scholar