Makarov, N. and Smirnov, S. (2003) On Thermodynamics of Rational Maps. II: Non-Recurrent Maps. Journal of the London Mathematical Society, 67 . pp. 417-432. ISSN 0024-6107 http://resolver.caltech.edu/CaltechAUTHORS:20111019-084131204
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The pressure function p(t) of a non-recurrent map is real analytic on some interval (0,t_*) with t_* strictly greater than the dimension of the Julia set. The proof is an adaptation of the well known tower techniques to the complex dynamics situation. In general, p(t) need not be analytic on the whole positive axis.
|Additional Information:||© 2003 London Mathematical Society. Received 13 September 2001; revised 18 April 2002. The first author is supported by NSF grant DMS-9800714. The second author is supported by the Göran Gustafssons Foundation and the Knut and Alice Wallenberg Foundation. The authors would like to thank Misha Lyubich and Marius Urbanski for useful discussions. Recently, Urbanski  gave an alternative proof of Theorem A based on his theory of conformal iteration systems. His ongoing project with Lyubich provides yet another approach, which uses the Lyubich and Minsky construction of hyperbolic laminations .|
|Classification Code:||2000 Mathematics Subject Classification: 37F, 37A, 30C85.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||26 Oct 2011 18:00|
|Last Modified:||26 Dec 2012 14:17|
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