Saurabh Verma - Böcker

This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14-15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.

This volume contains the proceedings of the AMS Special Session on Fractal Geometry and Dynamical Systems, held at the Spring Eastern Virtual Sectional Meeting on April 1-2, 2023, and the virtual Conference on Functional Analysis and Fractals organized by the Indian Institute of Information Technology Allahabad (IIIT-A), India, on February 16-18, 2024. Fifty years ago, Mandelbrot created a new type of geometry called fractal. One of the novelties of this new mathematics is a systematic qualitative and quantitative approach to the concepts of irregular shapes and roughness. Galileo said that the universe is written in mathematical language and its characters are triangles, circles, and ""other"" geometric figures. Mandelbrot masterly defined ""other"" geometric objects whose main property is the self-similarity and coined the term ""fractal"" for them. Such models fit better complex patterns such as the circulatory system, the coastline of a littoral country or a stock market chart. One way of quantifying the complexity of such structures is the computation of their fractal dimension. This book presents modern advances in the concept of dimension and its related notion of fractal measure. The text is oriented to give insight into the current research in the area, and it contains novel contributions of important scientists in the field. The book deals with very diverse topics such as the Hausdorff dimension of a set of continued fractions, dimension theory of inhomogeneous attractors, ergodic conjecture of falling balls systems, or Hausdorff measures to represent uncertainty in neural networks.