In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
1138412226
ANALYSIS, PROBABILITY AND MATHEMATICAL PHYSICS ON FRACTALS
In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
126.0
In Stock
5
1
ANALYSIS, PROBABILITY AND MATHEMATICAL PHYSICS ON FRACTALS
596
ANALYSIS, PROBABILITY AND MATHEMATICAL PHYSICS ON FRACTALS
596Related collections and offers
126.0
In Stock
Product Details
| ISBN-13: | 9789811215544 |
|---|---|
| Publisher: | World Scientific Publishing Company, Incorporated |
| Publication date: | 02/26/2020 |
| Series: | FRACTALS & DYNAMICS IN MATH, SCIENCE, & THE ARTS , #5 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 596 |
| File size: | 16 MB |
| Note: | This product may take a few minutes to download. |
From the B&N Reads Blog