The aim of this book is to provide a basic and self-contained introduction to the ideas underpinning fractal analysis. The book illustrates some important applications issued from real data sets, real physical and natural phenomena as well as real applications in different fields, and consequently, presents to the readers the opportunity to implement fractal analysis in their specialties according to the step-by-step guide found in the book.Besides advanced undergraduate students, graduate students and senior researchers, this book may also serve scientists and research workers from industrial settings, where fractals and multifractals are required for modeling real-world phenomena and data, such as finance, medicine, engineering, transport, images, signals, among others.For the theorists, rigorous mathematical developments are established with necessary prerequisites that make the book self-containing. For the practitioner often interested in model building and analysis, we provide the cornerstone ideas.
Contents:
- Preface
- About the Authors
- List of Figures
- List of Table
- Introduction
- Basics of Measure Theory
- Martingales with Discrete Time
- Hausdorff Measure and Dimension
- Capacity Dimension of Sets
- Packing Measure and Dimension
- Multifractal Analysis of Gibbs Type Measures
- Extensions to Multifractal Cases
- Some Applications
- Bibliography
- Index
Readership: Young researchers at master's level in sciences; researchers in PhD studies in pure and applied mathematical/physical sciences; and researchers at advanced levels are provided the necessary tools that allow them to understand and adapt fractal analysis to their needs such as supervision and development of research projects. Advanced undergraduate students will gain a clear idea on what fractal analysis is, that will guide them to decide their course on their future scientific research areas. It is applicable to the industrial and professional sectors such as ready-made constructions, town planning, such as construction and the development of plans for urban areas (fractal cities); for economists to develop good forecasting models and for researchers in nanofractal materials, geology, geosciences, biology, among others.
Key Features:
- The aim is to expose concepts underpinning fractal analysis for a common scientific community from different branches
- For theorists and applied researchers from a wide range of scientific fields, including pure mathematics, physics, statistics, time series, medicine, and econo-financial sciences
- Provides a step-by-step guide to the understanding of fractal analysis and its applications in other fields
- Provides a self-contained coverage of mathematical concepts as well as their proofs and does not require a strong previous background to be understood especially for postgraduate levels
