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Journal of the London Mathematical Society (1)

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ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
N. MAKAROV, S. SMIRNOV
Journal:

Journal of the London Mathematical Society / Volume 67 / Issue 2 / April 2003

Published online by Cambridge University Press:

24 March 2003, pp. 417-432

Print publication:

April 2003
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The pressure function $p(t)$ of a non-recurrent map is real analytic on some interval ($0,t_\ast$) with $t_\ast$ 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.