Author : Balázs Bárány,Károly Simon,Boris Solomyak
Publisher : American Mathematical Society
Page : 466 pages
File Size : 42,9 Mb
Release : 2023-11-16
Category : Mathematics
ISBN : 9781470470463
Self-similar and Self-affine Sets and Measures by Balázs Bárány,Károly Simon,Boris Solomyak Pdf
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.