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

Makarov, N.

Smirnov, S.

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Caltech Authors - Main

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

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https://authors.library.caltech.edu/27293/1/MAKjlms03.pdf

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

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