Published April 2003
| Published
Journal Article
Open
On Thermodynamics of Rational Maps. II: Non-Recurrent Maps
- Creators
- Makarov, N.
- Smirnov, S.
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.
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].Attached Files
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Additional details
- Eprint ID
- 27293
- Resolver ID
- CaltechAUTHORS:20111019-084131204
- DMS-9800714
- NSF
- Göran Gustafssons Foundation
- Knut and Alice Wallenberg Foundation
- Created
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2011-10-26Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field