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On Thermodynamics of Rational Maps. II: Non‐Recurrent Maps
Author(s) -
Makarov N.,
Smirnov S.
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003964
Subject(s) - julia set , interval (graph theory) , dimension (graph theory) , mathematics , set (abstract data type) , tower , function (biology) , thermodynamics , pure mathematics , computer science , combinatorics , physics , geography , evolutionary biology , biology , archaeology , programming language
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.
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