Differential Equations on Fractals: A Tutorial
Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels o...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2018]
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| Schlagworte: | |
| Online-Zugang: | FHA01 FKE01 FLA01 UPA01 FAW01 FAB01 FCO01 Volltext |
| Zusammenfassung: | Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018) |
| Beschreibung: | 1 online resource |
| ISBN: | 9780691186832 |
| DOI: | 10.1515/9780691186832 |
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| language | English |
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| spelling | Strichartz, Robert S. Verfasser aut Differential Equations on Fractals A Tutorial Robert S. Strichartz Princeton, NJ Princeton University Press [2018] © 2006 1 online resource txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018) Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course In English Differential equations Fractals Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktal (DE-588)4123220-3 s Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 https://doi.org/10.1515/9780691186832 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Strichartz, Robert S. Differential Equations on Fractals A Tutorial Differential equations Fractals Differentialgleichung (DE-588)4012249-9 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4123220-3 |
| title | Differential Equations on Fractals A Tutorial |
| title_auth | Differential Equations on Fractals A Tutorial |
| title_exact_search | Differential Equations on Fractals A Tutorial |
| title_full | Differential Equations on Fractals A Tutorial Robert S. Strichartz |
| title_fullStr | Differential Equations on Fractals A Tutorial Robert S. Strichartz |
| title_full_unstemmed | Differential Equations on Fractals A Tutorial Robert S. Strichartz |
| title_short | Differential Equations on Fractals |
| title_sort | differential equations on fractals a tutorial |
| title_sub | A Tutorial |
| topic | Differential equations Fractals Differentialgleichung (DE-588)4012249-9 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Differential equations Fractals Differentialgleichung Fraktal |
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