LECTURES ON FRACTAL GEOMETRY

This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.

This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.

Contents:

• Measure Theoretic Foundations
• Hausdorff and Packing Measures
• Upper and Lower Densities of Measures and Comparison with Hausdorff and Packing Measures
• Hausdorff Dimension and Potential Theory
• Other Fractal Dimensions
• Dimensions of Borel Measures
• Attractors of Iterated Function Systems
• An Example from the Theory of Dynamical Systems
• Graphs of Functions and Stochastic Processes

Readership: The book is suited for Master and PhD students, but also for mathematicians from other fields interested in fractals. While basic knowledge on general measure theory and on topological notions in metric spaces is presumed, for courses the material can also be restricted to the Euclidean setting. Some of the exercises are included.

Key Features:

• Aims to give a profound introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications
• Suited for Masters and PhD students, but also for mathematicians from other fields interested in fractals
• For courses the material can also be restricted to the Euclidean setting. Some of the exercises are included