Non-Invertible Dynamical Systems. Finer Thermodynamic Formalism – Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry / / Mariusz Urbański, Mario Roy, Sara Munday.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• VerfasserIn: Urbański, Mariusz,; Munday, Sara,; Roy, Mario,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: De Gruyter Expositions in Mathematics , 69/2
• Physical Description: 1 online resource (XXX, 494 p.)

This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere.

Table of Contents

Frontmatter -- Preface -- List of Figures -- Introduction to Volume 2 -- Contents -- 13 Gibbs states and transfer operators for open, distance expanding systems -- 14 Lasota–Yorke maps -- 15 Fractal measures and dimensions -- 16 Conformal expanding repellers -- 17 Countable state thermodynamic formalism -- 18 Countable state thermodynamic formalism: finer properties -- 19 Conformal graph directed Markov systems -- 20 Real analyticity of topological pressure and Hausdorff dimension -- 21 Multifractal analysis for conformal graph directed Markov systems -- Appendix A – A selection of classical results -- Appendix B – The Ionescu-Tulcea and Marinescu theorem -- Bibliography -- Index