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On Thermodynamics of Rational Maps. II: Non-Recurrent Maps

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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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1112/S0024610702003964DOIUNSPECIFIED
http://jlms.oxfordjournals.org/content/67/2/417PublisherUNSPECIFIED
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 [10] 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 [6].
Funders:
Funding AgencyGrant Number
NSFDMS-9800714
Göran Gustafssons FoundationUNSPECIFIED
Knut and Alice Wallenberg FoundationUNSPECIFIED
Classification Code:2000 Mathematics Subject Classification: 37F, 37A, 30C85.
Record Number:CaltechAUTHORS:20111019-084131204
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111019-084131204
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27293
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Oct 2011 18:00
Last Modified:26 Dec 2012 14:17

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