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Complex Analysis and Dynamical Systems

New Trends and Open Problems

  • Book
  • © 2018

Overview

Editors:
  1. Mark Agranovsky

    1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

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  2. Anatoly Golberg

    1. Department of Mathematics, Holon Institute of Technology, Holon, Israel

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  3. Fiana Jacobzon

    1. Department of Mathematics, ORT Braude College, Karmiel, Israel

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  4. David Shoikhet

    1. Department of Mathematics, Holon Institute of Technology, Holon, Israel

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  5. Lawrence Zalcman

    1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

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  • Contains expositions of numerous open problems in such important areas as complex dynamical systems, geometric function theory and harmonic analysis
  • Provides relevant background and historical remarks concerning these problems and their interrelationships
  • Dedicated to the memory of Alexander Vasiliev

Part of the book series: Trends in Mathematics (TM)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. On Polynomially Integrable Domains in Euclidean Spaces

    • Mark Agranovsky
    Pages 1-21

  3. A Survey on the Maximal Number of Solutions of Equations Related to Gravitational Lensing

    • Catherine Bénéteau, Nicole Hudson
    Pages 23-38

  4. Boundary Interpolation by Finite Blaschke Products

    • Vladimir Bolotnikov
    Pages 39-65

  5. Support Points and the Bieberbach Conjecture in Higher Dimension

    • Filippo Bracci, Oliver Roth
    Pages 67-79

  6. Some Unsolved Problems About Condenser Capacities on the Plane

    • Vladimir N. Dubinin
    Pages 81-92

  7. Filtration of Semi-complete Vector Fields Revisited

    • Mark Elin, David Shoikhet, Toshiyuki Sugawa
    Pages 93-102

  8. Polynomial Lemniscates and Their Fingerprints: From Geometry to Topology

    • Anastasia Frolova, Dmitry Khavinson, Alexander Vasil’ev
    Pages 103-128

  9. Regularity of Mappings with Integrally Restricted Moduli

    • Anatoly Golberg, Ruslan Salimov
    Pages 129-140

  10. Extremal Problems for Mappings with g-Parametric Representation on the Unit Polydisc in ℂn

    • Ian Graham, Hidetaka Hamada, Gabriela Kohr
    Pages 141-167

  11. Evolution of States of a Continuum Jump Model with Attraction

    • Yuri Kozitsky
    Pages 169-189

  12. Problems on Weighted and Unweighted Composition Operators

    • Valentin Matache
    Pages 191-217

  13. Harmonic Measures of Slit Sides, Conformal Welding and Extremum Problems

    • Dmitri Prokhorov
    Pages 219-230

  14. Comparison Moduli Spaces of Riemann Surfaces

    • Eric Schippers, Wolfgang Staubach
    Pages 231-271

  15. Asymptotic Ratio of Harmonic Measures of Sides of a Boundary Slit

    • Alexander Solynin
    Pages 273-299

  16. Coupling of Gaussian Free Field with General Slit SLE

    • Alexey Tochin, Alexander Vasil’ev
    Pages 301-366

  17. A Marx-Strohhacker Type Result for Close-to-Convex Functions

    • Nikola Tuneski, Mamoru Nunokawa, Biljana Jolevska-Tuneska
    Pages 367-372
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Keywords

About this book

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences.

Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves.

This volume is dedicated to the memory of Alexander Vasiliev.

Editors and Affiliations

  • Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Mark Agranovsky, Lawrence Zalcman

  • Department of Mathematics, Holon Institute of Technology, Holon, Israel

    Anatoly Golberg, David Shoikhet

  • Department of Mathematics, ORT Braude College, Karmiel, Israel

    Fiana Jacobzon

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