000			01689nam a22001817a 4500
003			OSt
005			20250711183947.0
008			240301b |||||||| |||| 00| 0 eng d
020			_a9781470470463
082			_a516.3 _bBAR
100			_aBarany, Balazs
245			_aSelf -Similar and Self-affine Sets and Measures/ _cBalazs Barany, Karoly Simon and Boris Solomyak
260			_aProvidence, Rhode Island: _bAmerican Mathematical Society, _c2023.
300			_axii,451p.
490			_aMathematical Surveys and Monographs Volume 276
520			_aAlthough 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.
942			_2ddc _cBK
999			_c23063 _d23063