Non-Invertible Dynamical Systems. / Volume 3, : Analytic Endomorphisms of the Riemann Sphere / / Mariusz Urbański, Mario Roy, Sara Munday.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1
• VerfasserIn: Urbański, Mariusz,; Munday, Sara,; Roy, Mario,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2023]; ©2023
• Year of Publication: 2023
• Language: English
• Series: De Gruyter Expositions in Mathematics , 69/3
• Physical Description: 1 online resource (XXVIII, 412 p.)
• Other title: Frontmatter --; Preface --; List of Figures --; Introduction to Volume 3 --; Contents --; Volume 3 --; 22 The Riemann–Hurwitz formula --; 23 Selected tools from complex analysis --; 24 Dynamics and topology of rational functions: their Fatou and Julia sets --; 25 Selected technical properties of rational functions --; 26 Expanding (or hyperbolic), subexpanding, and parabolic rational functions: topological outlook --; 27 Equilibrium states for rational functions and Hölder continuous potentials with pressure gap --; 28 Invariant measures: fractal and dynamical properties --; 29 Sullivan’s conformal measures for rational functions --; 30 Conformal measures, invariant measures and fractal geometry of expanding rational functions --; 31 Conformal measures, invariant measures and fractal geometry of parabolic rational functions --; 32 Conformal measures, invariant measures and fractal geometry of subexpanding rational functions --; Appendix A – A selection of classical results --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110769876; 9783111175782; 9783111319292; 9783111318912; 9783111319209; 9783111318608
• ISSN: 0938-6572
• DOI: 10.1515/9783110769876
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Mariusz Urbański, Mario Roy, Sara Munday.

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.