Complex Analysis and Dynamical Systems: New Trends and Open Problems

Description

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. Front Matter ....Pages i-viii On Polynomially Integrable Domains in Euclidean Spaces (Mark Agranovsky)....Pages 1-21 A Survey on the Maximal Number of Solutions of Equations Related to Gravitational Lensing (Catherine Bénéteau, Nicole Hudson)....Pages 23-38 Boundary Interpolation by Finite Blaschke Products (Vladimir Bolotnikov)....Pages 39-65 Support Points and the Bieberbach Conjecture in Higher Dimension (Filippo Bracci, Oliver Roth)....Pages 67-79 Some Unsolved Problems About Condenser Capacities on the Plane (Vladimir N. Dubinin)....Pages 81-92 Filtration of Semi-complete Vector Fields Revisited (Mark Elin, David Shoikhet, Toshiyuki Sugawa)....Pages 93-102 Polynomial Lemniscates and Their Fingerprints: From Geometry to Topology (Anastasia Frolova, Dmitry Khavinson, Alexander Vasil’ev)....Pages 103-128 Regularity of Mappings with Integrally Restricted Moduli (Anatoly Golberg, Ruslan Salimov)....Pages 129-140 Extremal Problems for Mappings with g-Parametric Representation on the Unit Polydisc in ℂn (Ian Graham, Hidetaka Hamada, Gabriela Kohr)....Pages 141-167 Evolution of States of a Continuum Jump Model with Attraction (Yuri Kozitsky)....Pages 169-189 Problems on Weighted and Unweighted Composition Operators (Valentin Matache)....Pages 191-217 Harmonic Measures of Slit Sides, Conformal Welding and Extremum Problems (Dmitri Prokhorov)....Pages 219-230 Comparison Moduli Spaces of Riemann Surfaces (Eric Schippers, Wolfgang Staubach)....Pages 231-271 Asymptotic Ratio of Harmonic Measures of Sides of a Boundary Slit (Alexander Solynin)....Pages 273-299 Coupling of Gaussian Free Field with General Slit SLE (Alexey Tochin, Alexander Vasil’ev)....Pages 301-366 A Marx-Strohhacker Type Result for Close-to-Convex Functions (Nikola Tuneski, Mamoru Nunokawa, Biljana Jolevska-Tuneska)....Pages 367-372