This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.Read more
- This is the first book on a new area of mathematics, analysis on fractals
- No special knowledge of fractals required
- Self contained: covers basic background material as well as recent research
Reviews & endorsements
'… the most recent introduction to the analysis of 'Laplacians' on what physicists call finitely ramified self-similar fractals.' Volker Metz, Zentralblatt MATHSee more reviews
'Anyone with a background in the analysis of linear field equations, with an interest in heterogeneous media, or who is looking to breathe new life into their research, should read this book.' A. J. Mulholland, Proceedings of the Edinburgh Mathematical Society
'This book is an introduction to the subject written by one of the active researchers in the area. It is recommended to those who would like to go from the basics to current research topics.' Acta. Sci. Math.
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- Date Published: November 2010
- format: Paperback
- isbn: 9780521057110
- length: 236 pages
- dimensions: 229 x 152 x 14 mm
- weight: 0.35kg
- contains: 12 b/w illus.
- availability: Available
Table of Contents
1. Geometry of self-similar sets
2. Analysis on limits of networks
3. Construction of Laplacians on P. C. F. self-similar structures
4. Eigenvalues and eigenfunctions of Laplacians
5. Heat kernels
Appendix A: Additional fact
Appendix B: Mathematical backgrounds
List of notations
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