Self-similar and self-affine sets and measures:
Although there is no precise definition of a "fractal", it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transforma...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2023]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 276 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Although there is no precise definition of a "fractal", it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses. |
| Beschreibung: | Includes bibliographical references and index Literaturverzeichnis: Seite 429-445 |
| Beschreibung: | 1 Online-Ressource (xii, 451 Seiten) Diagramme |
| ISBN: | 9781470475505 9781470470463 |
| DOI: | 10.1090/surv/276 |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 276 | |
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| 520 | 3 | |a Although there is no precise definition of a "fractal", it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses. | |
| 653 | 0 | |a Self-similar processes | |
| 653 | 0 | |a Fractals | |
| 653 | 0 | |a Hausdorff measures | |
| 653 | 0 | |a Measure and integration -- Classical measure theory -- Fractals | |
| 653 | 0 | |a Measure and integration -- Classical measure theory -- Hausdorff and packing measures | |
| 653 | 0 | |a Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory | |
| 653 | 0 | |a Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Thermodynamic formalism, variational principles, equilibrium states | |
| 653 | 0 | |a Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type | |
| 700 | 1 | |a Simon, Károly |d 1961- |0 (DE-588)1322431809 |4 aut | |
| 700 | 1 | |a Solomyak, Boris |4 aut | |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1090/surv/276 |
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| id | DE-604.BV050066015 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-28T11:09:34Z |
| institution | BVB |
| isbn | 9781470475505 9781470470463 |
| language | English |
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| physical | 1 Online-Ressource (xii, 451 Seiten) Diagramme |
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| publisher | American Mathematical Society |
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| spelling | Bárány, Balázs 1984- (DE-588)1322590370 aut Self-similar and self-affine sets and measures Balázs Bárány, ; Károly Simon ; Boris Solomyak Providence, Rhode Island American Mathematical Society [2023] © 2023 1 Online-Ressource (xii, 451 Seiten) Diagramme txt rdacontent c rdamedia cr rdacarrier Mathematical surveys and monographs Volume 276 Includes bibliographical references and index Literaturverzeichnis: Seite 429-445 Although there is no precise definition of a "fractal", it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses. Self-similar processes Fractals Hausdorff measures Measure and integration -- Classical measure theory -- Fractals Measure and integration -- Classical measure theory -- Hausdorff and packing measures Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Thermodynamic formalism, variational principles, equilibrium states Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Simon, Károly 1961- (DE-588)1322431809 aut Solomyak, Boris aut Erscheint auch als Druck-Ausgabe 978-1-4704-7046-3 Mathematical surveys and monographs Volume 276 (DE-604)BV042339669 276 https://doi.org/10.1090/surv/276 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Bárány, Balázs 1984- Simon, Károly 1961- Solomyak, Boris Self-similar and self-affine sets and measures Mathematical surveys and monographs |
| title | Self-similar and self-affine sets and measures |
| title_auth | Self-similar and self-affine sets and measures |
| title_exact_search | Self-similar and self-affine sets and measures |
| title_full | Self-similar and self-affine sets and measures Balázs Bárány, ; Károly Simon ; Boris Solomyak |
| title_fullStr | Self-similar and self-affine sets and measures Balázs Bárány, ; Károly Simon ; Boris Solomyak |
| title_full_unstemmed | Self-similar and self-affine sets and measures Balázs Bárány, ; Károly Simon ; Boris Solomyak |
| title_short | Self-similar and self-affine sets and measures |
| title_sort | self similar and self affine sets and measures |
| url | https://doi.org/10.1090/surv/276 |
| volume_link | (DE-604)BV042339669 |
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