Meromorphic Dynamics: Volume 1

Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures

Inbunden, Engelska, 2023

Av Janina Kotus, Mariusz Urbański, Mariusz Urbański, Janina (Warsaw University of Technology) Kotus, Mariusz (University of North Texas) Urbanski, Urba&

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This text, the first of two volumes, provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students.

Produktinformation

Utgivningsdatum2023-05-04
Mått156 x 235 x 31 mm
Vikt850 g
FormatInbunden
SpråkEngelska
SerieNew Mathematical Monographs
Antal sidor420
FörlagCambridge University Press
ISBN9781009215916

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Janina Kotus is Professor of Mathematics at the Warsaw University of Technology, Poland. Her research focuses on dynamical systems, in particular holomorphic dynamical systems. Together with I. N. Baker and Y. Lű she laid the foundations for iteration of meromophic functions. Mariusz Urbański is Professor of Mathematics at the University of North Texas. His research interests include dynamical systems, ergodic theory, fractal geometry, iteration of rational and meromorphic functions, open dynamical systems, iterated function systems, Kleinian groups, diophantine approximations, topology and thermodynamic formalism. He is the author of eight books, seven monographs, and more than 200 papers.

Volume I. Preface; Acknowledgments; Introduction; Part I. Ergodic Theory and Geometric Measures: 1. Geometric measure theory; 2. Invariant measures: finite and infinite; 3. Probability (finite) invariant measures: basic properties and existence; 4. Probability (finite) invariant measures: finer properties; 5. Infinite invariant measures: finer properties; 6. Measure- theoretic entropy; 7. Thermodynamic formalism; Part II. Complex Analysis, Conformal Measures, and Graph Directed Markov Systems: 8. Selected topics from complex analysis; 9. Invariant measures for holomorphic maps f in A(X) or in Aw(X); 10. Sullivan conformal measures for holomorphic maps f in A(X) and in Aw(X); 11. Graph directed Markov systems; 12. Nice sets for analytic maps; References; Index of symbols; Subject index; Volume II. Preface; Acknowledgments; Introduction; Part III. Topological Dynamics of Meromorphic Functions: 13. Fundamental properties of meromorphic dynamical systems; 14. Finer properties of fatou components; 15. Rationally indifferent periodic points; Part IV. Elliptic Functions: Classics, Geometry, and Dynamics: 16. Classics of elliptic functions: selected properties; 17. Geometry and dynamics of (all) elliptic functions.