Details

Subject(s)

• Self-similar processes [Browse]
• Fractals [Browse]
• Hausdorff measures [Browse]

Author

• Simon, Károly, 1961- [Browse]
• Solomyak, Boris, 1959- [Browse]

Series

• Mathematical surveys and monographs ; no. 276. [More in this series]
• Mathematical surveys and monographs, 0076-5376 ; Volume 276 [More in this series]

Summary note

"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"-- Publisher's website.

Bibliographic references

Includes bibliographical references (pages 429-445) and index.

ISBN

• 9781470470463 (paperback)
• 1470470462 (paperback)

LCCN

2023030385

OCLC

1401628230

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