The geometry of fractal sets:
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various direct...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1985
|
| Schriftenreihe: | Cambridge tracts in mathematics
85 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods |
| Beschreibung: | 1 Online-Ressource (xiv, 162 Seiten) |
| ISBN: | 9780511623738 |
| DOI: | 10.1017/CBO9780511623738 |
Internformat
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| 520 | |a This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Falconer, Kenneth J. 1952- |
| author_GND | (DE-588)112970613 |
| author_facet | Falconer, Kenneth J. 1952- |
| author_role | aut |
| author_sort | Falconer, Kenneth J. 1952- |
| author_variant | k j f kj kjf |
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| bvnumber | BV043940681 |
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| ctrlnum | (ZDB-20-CBO)CR9780511623738 (OCoLC)859645098 (DE-599)BVBBV043940681 |
| dewey-full | 515/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.64 |
| dewey-search | 515/.64 |
| dewey-sort | 3515 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511623738 |
| format | Electronic eBook |
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| id | DE-604.BV043940681 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511623738 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349651 |
| oclc_num | 859645098 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xiv, 162 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Falconer, Kenneth J. 1952- Verfasser (DE-588)112970613 aut The geometry of fractal sets K.J. Falconer Cambridge Cambridge University Press 1985 1 Online-Ressource (xiv, 162 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 85 This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods Fractals Geometric measure theory Geometrie (DE-588)4020236-7 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktalgeometrie (DE-588)4473576-5 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Fraktal (DE-588)4123220-3 s Maßtheorie (DE-588)4074626-4 s DE-604 Geometrie (DE-588)4020236-7 s Fraktalgeometrie (DE-588)4473576-5 s Erscheint auch als Druck-Ausgabe 978-0-521-25694-0 Erscheint auch als Druck-Ausgabe 978-0-521-33705-2 https://doi.org/10.1017/CBO9780511623738 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Falconer, Kenneth J. 1952- The geometry of fractal sets Fractals Geometric measure theory Geometrie (DE-588)4020236-7 gnd Fraktal (DE-588)4123220-3 gnd Fraktalgeometrie (DE-588)4473576-5 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4123220-3 (DE-588)4473576-5 (DE-588)4074626-4 |
| title | The geometry of fractal sets |
| title_auth | The geometry of fractal sets |
| title_exact_search | The geometry of fractal sets |
| title_full | The geometry of fractal sets K.J. Falconer |
| title_fullStr | The geometry of fractal sets K.J. Falconer |
| title_full_unstemmed | The geometry of fractal sets K.J. Falconer |
| title_short | The geometry of fractal sets |
| title_sort | the geometry of fractal sets |
| topic | Fractals Geometric measure theory Geometrie (DE-588)4020236-7 gnd Fraktal (DE-588)4123220-3 gnd Fraktalgeometrie (DE-588)4473576-5 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Fractals Geometric measure theory Geometrie Fraktal Fraktalgeometrie Maßtheorie |
| url | https://doi.org/10.1017/CBO9780511623738 |
| work_keys_str_mv | AT falconerkennethj thegeometryoffractalsets |