Zinsmeister, Michel Thermodynamic formalism and holomorphic dynamical systems. Transl. from the French by C. Greg Anderson. (English) Zbl 0959.37003 SMF/AMS Texts and Monographs. 2. Providence, RI: American Mathematical Society (AMS). Paris: Société Mathématique de France, ix, 82 p. (2000). The present book is a slightly revised English translation of the original French version [Société Mathématique de France (1996; Zbl 0879.58042)]. The main changes occur in Chapters 5 and 6 and consist in clarification of some proofs and a new presentation of the basics in iterations of polynomials. Reviewer: N.Papaghiuc (Iaşi) Cited in 21 Documents MSC: 37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory 37Axx Ergodic theory 28Dxx Measure-theoretic ergodic theory 37F50 Small divisors, rotation domains and linearization in holomorphic dynamics 37F75 Dynamical aspects of holomorphic foliations and vector fields 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 82B26 Phase transitions (general) in equilibrium statistical mechanics 37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems Keywords:entropy; ergodic theory; thermodynamical formalism; Julia set; Perron-Frobenius-Ruelle theorem; iterating quadratic polynomials; Hausdorff-dimension; phase transition Citations:Zbl 0879.58042 PDFBibTeX XMLCite \textit{M. Zinsmeister}, Thermodynamic formalism and holomorphic dynamical systems. Transl. from the French by C. Greg Anderson. Providence, RI: American Mathematical Society; Paris: Société Mathématique de France (2000; Zbl 0959.37003)