Mathematics of fractals:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1997
|
| Series: | Translations of mathematical monographs
167 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Japan. übers. |
| Physical Description: | VII, 78 S. Ill., graph. Darst. |
| ISBN: | 0821805371 |
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MARC
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| 245 | 1 | 0 | |a Mathematics of fractals |c Masaya Yamaguti ; Masayoshi Hata ; Jun Kigami |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Preface to the English Translation xi
Chapter 1. The Fundamentals of Fractals 1
1.1. What is the dimension? 1
1.2. Hausdorff measure and Hausdorff dimension 4
1.3. Examples of fractals and their Hausdorff dimensions 7
1.4. Nowhere differentiable functions 11
Exercises 14
Chapter 2. Self Similar Sets 17
2.1. Existence and uniqueness 17
2.2. The size and shape of a self similar set 20
2.3. Self amne sets 26
2.4. Fractals and chaos 29
Exercises 30
Chapter 3. An Alternative Computation for Differentiation 33
3.1. A chaotic dynamical system and its generating function 33
3.2. The Schauder expansion 36
3.3. The de Rham equations and Lebesgue s singular function 38
3.4. The system of difference equations of Lebesgue s function 41
3.5. The relation between T{x) and Ma{x) and its generalization 44
3.6. Wavelet expansions 47
Exercises 51
Chapter 4. In Quest of Fractal Analysis 53
4.1. The Sierpinski gasket 53
4.2. The wave equation on the Sierpinski gasket.
A physical observation 59
4.3. The Laplacian on the Sierpinski gasket
and a Gauss Green type theorem 63
4.4. The Dirichlet problem for Poisson s equation 68
Exercises 72
Recommended Reading 75
Index 77
vii
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| id | DE-604.BV011795171 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:53Z |
| institution | BVB |
| isbn | 0821805371 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007962794 |
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| physical | VII, 78 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Yamaguti, Masaya Verfasser aut Furakutaru no sūri Mathematics of fractals Masaya Yamaguti ; Masayoshi Hata ; Jun Kigami Providence, RI American Math. Soc. 1997 VII, 78 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 167 Aus dem Japan. übers. Chaotic behavior in systems Fractals Chaostheorie (DE-588)4009754-7 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktal (DE-588)4123220-3 s Chaostheorie (DE-588)4009754-7 s DE-604 Hata, Masayoshi Verfasser aut Kigami, Jun Verfasser aut Translations of mathematical monographs 167 (DE-604)BV000002394 167 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007962794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yamaguti, Masaya Hata, Masayoshi Kigami, Jun Mathematics of fractals Translations of mathematical monographs Chaotic behavior in systems Fractals Chaostheorie (DE-588)4009754-7 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4123220-3 |
| title | Mathematics of fractals |
| title_alt | Furakutaru no sūri |
| title_auth | Mathematics of fractals |
| title_exact_search | Mathematics of fractals |
| title_full | Mathematics of fractals Masaya Yamaguti ; Masayoshi Hata ; Jun Kigami |
| title_fullStr | Mathematics of fractals Masaya Yamaguti ; Masayoshi Hata ; Jun Kigami |
| title_full_unstemmed | Mathematics of fractals Masaya Yamaguti ; Masayoshi Hata ; Jun Kigami |
| title_short | Mathematics of fractals |
| title_sort | mathematics of fractals |
| topic | Chaotic behavior in systems Fractals Chaostheorie (DE-588)4009754-7 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Chaotic behavior in systems Fractals Chaostheorie Fraktal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007962794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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