"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…mehr
"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"--Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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 Part V. Compactly Nonrecurrent Elliptic Functions: First Outlook: 18. Dynamics of compactly norecurrent elliptic functions 19. Various examples of compactly nonrecurrent elliptic functions Part VI. Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity: 20. Sullivan h-conformal measures for compactly nonrecurrent elliptic functions 21. Hausdorff and packing measures of compactly nonrecurrent regular elliptic functions 22. Conformal invariant measures for compactly nonrecurrent regular elliptic functions 23. Dynamical rigidity of compactly nonrecurrent regular elliptic functions Appendix A. A quick review of some selected facts from complex analysis of a one-complex variable Appendix B. Proof of the Sullivan nonwandering theorem for speiser class S References Index of symbols Subject index.
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 Part V. Compactly Nonrecurrent Elliptic Functions: First Outlook: 18. Dynamics of compactly norecurrent elliptic functions 19. Various examples of compactly nonrecurrent elliptic functions Part VI. Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity: 20. Sullivan h-conformal measures for compactly nonrecurrent elliptic functions 21. Hausdorff and packing measures of compactly nonrecurrent regular elliptic functions 22. Conformal invariant measures for compactly nonrecurrent regular elliptic functions 23. Dynamical rigidity of compactly nonrecurrent regular elliptic functions Appendix A. A quick review of some selected facts from complex analysis of a one-complex variable Appendix B. Proof of the Sullivan nonwandering theorem for speiser class S References Index of symbols Subject index.
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