Janina Kotus, Urba &

Meromorphic Dynamics: Volume 1

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

• Gebundenes Buch

Produktbeschreibung

"The second of two volumes builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental meromorphic functions, before progressing to elliptic functions, discussing at length their classical properties, measurable dynamics and fractal geometry. The authors then look in depth at compactly non-recurrent elliptic functions. Much of this material is appearing for the first time in book or paper form. Both senior and junior researchers working in ergodic theory and dynamical systems will appreciate what is sure to be an indispensable reference"--

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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 420
• Erscheinungstermin: 6. Juli 2023
• Englisch
• Abmessung: 234mm x 156mm x 33mm
• Gewicht: 860g
• ISBN-13: 9781009215916
• ISBN-10: 1009215914
• Artikelnr.: 65769634

Autorenporträt

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. L¿ she laid the foundations for iteration of meromophic functions.

Inhaltsangabe

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.