Self-similar and Self-affine Sets and Measures
American Mathematical Society (Verlag)
978-1-4704-7046-3 (ISBN)
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.
Balazs Barany, Budapest University of Technology and Economics, Hungary. Karoly Simon, Budapest University of Technology and Economics, Hungary. Boris Solomyak, Bar-Ilan University, Ramat Gan, Israel.
Introduction
Elements of geometric measure theory
General properties of self-similar sets and measures
Separation properties for self-similar IFS
Multifractal analysis for self-similar measures
Transversality techniques for self-similar IFS
Further properties of self-similar IFS with overlaps
Fourier-analytic and number-theoretic methods
Elements of ergodic theory
Self-affine sets and measures
Diagonally self-affine IFS
Exact dimensionality and dimension conservation
Local entropy averages and projections of self-affine sets and measures
Nonlinear conformal iterated functions systems
Some elements of linear algebras
Some elements of measure theory
Some elements of harmonic analysis
Some acts about algebraic numbers
Bibliography
Index
Basic notation
| Erscheinungsdatum | 05.12.2023 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 399 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-7046-2 / 1470470462 |
| ISBN-13 | 978-1-4704-7046-3 / 9781470470463 |
| Zustand | Neuware |
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