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Phase transition in subhyperbolic Julia sets

Published online by Cambridge University Press:  19 September 2008

N. Makarov  and
S. Smirnov
N. Makarov
Affiliation:
California Institute of Technology, 253–37 Pasadena, CA 91125, USA
S. Smirnov
Affiliation:
California Institute of Technology, 253–37 Pasadena, CA 91125, USA
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Abstract

We study the pressure function for critically finite polynomials and analyze the case when this function fails to be real analytic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996 , pp. 125 - 157
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

[B]Bowen, R.. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Mathematics 470. Springer, Berlin, 1975.CrossRefGoogle Scholar
[CJ]Carleson, L. and Jones, P. W.. On the coefficient problems for univalent functions and conformal dimension. Duke Math. J. 66 (1992), 169–206.CrossRefGoogle Scholar
[HK]Hofbauer, F. and Keller, G.. Ergodic properties of invariant measures for piecewise monotonic transformations. Math. Z. 180 (1982), 119–140.CrossRefGoogle Scholar
[Ma]Makarov, N. G.. Probability methods in the theory of conformal mappings. Leningrad Math. J. 1 (1990), 1–56.Google Scholar
[M]Milnor, J.. Dynamics in one complex variable: introductory lectures SUNY. Stony Brook Institute for Mathematical Sciences, Preprints 5 (1990).Google Scholar
[P]Pollicott, M.. A complex Ruelle-Perron-Frobenius theorem and two counterexamples. Ergod. Th. & Dynam. Sys. 4 (1984), 135–146.CrossRefGoogle Scholar
[Pom]Pommerenke, Ch.. Boundary Behaviour of Conformed Maps. Springer, Berlin, 1992.CrossRefGoogle Scholar
[R1]Ruelle, D.. Thermodynamic Formalism. Addison-Wesley, Reading, MA, 1978.Google Scholar
[R2]Ruelie, D.. Repellers for real analytic maps. Ergod. Th. & Dynam. Sys. 2 (1982), 99–107'.CrossRefGoogle Scholar
[Ry]Rychlik, M.. Bounded variation and invariant measures. Studia Math. LXXVI (1983), 69–80.CrossRefGoogle Scholar