Thermodynamic Formalism And Holomorphic Dynamical Systems

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Thermodynamic Formalism and Holomorphic Dynamical Systems

Author: Michel Zinsmeister
language: en
Publisher: American Mathematical Soc.
Release Date: 2000
Thermodynamics helps in understanding the equilibrium of a gas or the different states of matter, and recently it has also become a powerful tool for understanding the objects of holomorphic dynamical systems. While the reasons remain obscure, this book begins to describe the physical and mathematical aspects of this relationship in order to understand how it works and how useful it can be. Annotation copyrighted by Book News, Inc., Portland, OR
Thermodynamic Formalism

This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Analytic Endomorphisms of the Riemann Sphere

Author: Mariusz Urbański
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2023-09-05
Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of rational functions on the Riemann sphere (in particular, the Fatou and Julia sets) but also focuses on thermodynamic, ergodic and fractal properties of these functions (notably, equilibrium states, Bowen's formula and Sullivan’s conformal measures). This volume builds on the first two volumes in the series while simultaneously developing some methods and techniques specific to rational functions.