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LEADER 03736cam 2200613 i 4500

001 on1401628230;

003 OCoLC;

005 20240430153554.0;

008 230711s2023 riua b 001 0 eng ;

010 a| 2023030385;

020 a| 9781470470463q| paperback;

020 a| 1470470462q| paperback;

020 z| 9781470475505q| electronic book;

035 a| (Sirsi) 40032133479;

035 a| 40032133479;

035 a| (OCoLC)1401628230;

042 a| pcc;

050 00 a| QA274.9b| .B37 2023;

082 00 a| 519.2/32| 23/eng/20231002;

084 a| 28A80a| 28A78a| 28A75a| 37D35a| 42A382| msc;

100 1 a| Bárány, Balázs,d| 1984-e| author.=| ^A1466182;

245 10 a| Self-similar and self-affine sets and measures /c| Balázs Bárány, Károly Simon, Boris Solomyak.;

264 1 a| Providence, Rhode Island :b| American Mathematical Society,c| [2023];

300 a| xii, 451 pages :b| illustrations (some color) ;c| 26 cm.;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

490 1 a| Mathematical surveys and monographs,x| 0076-5376 ;v| Volume 276;

504 a| Includes bibliographical references (pages 429-445) and index.;

520 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"--c| Publisher's website.;

650 0 a| Self-similar processes.=| ^A1234166;

650 0 a| Fractals.=| ^A187351;

650 0 a| Hausdorff measures.=| ^A65793;

650 6 a| Processus autosimilaires.;

650 6 a| Fractales.;

650 6 a| Mesures de Hausdorff.;

650 7 a| fractals.2| aat;

650 7 a| Fractals.2| fast;

650 7 a| Hausdorff measures.2| fast;

650 7 a| Self-similar processes.2| fast;

650 7 a| Measure and integration -- Classical measure theory -- Fractals.2| msc;

650 7 a| Measure and integration -- Classical measure theory -- Hausdorff and packing measures.2| msc;

650 7 a| Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory.2| msc;

650 7 a| Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Thermodynamic formalism, variational principles, equilibrium states.2| msc;

650 7 a| Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type.2| msc;

700 1 a| Simon, Károly,d| 1961-e| author.=| ^A1468666;

700 1 a| Solomyak, Boris,d| 1959-e| author.=| ^A1467154;

830 0 a| Mathematical surveys and monographsv| no. 276.=| ^A638333;

949 i| 30372017710424o| jjlm;

960 o| 1s| 129.00t| Joyner48u| JAPPz| USD;

596 a| 1;

998 a| 6313321;

999 a| QA274.9 .B37 2023w| LCc| 1i| 30372017710424d| 7/1/2024e| 3/3/2024l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 3/2/2024x| BOOKz| JSTACKSo| .STAFF. jjlm;

Self-similar and self-affine sets and measures / Balázs Bárány, Károly Simon, Boris Solomyak.

Author/creator	Bárány, Balázs, 1984- author.
Other author	Simon, Károly, 1961- author.
Other author	Solomyak, Boris, 1959- author.
Format	Book
Publication	Providence, Rhode Island : American Mathematical Society, [2023]
Description	xii, 451 pages : illustrations (some color) ; 26 cm.
Subjects	Self-similar processes. Fractals. Hausdorff measures. Processus autosimilaires. Fractales. Mesures de Hausdorff.

Series	Mathematical surveys and monographs, 0076-5376 ; Volume 276 Mathematical surveys and monographs no. 276. ^A638333
Abstract	"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.
Bibliography note	Includes bibliographical references (pages 429-445) and index.
LCCN	2023030385
ISBN	9781470470463 paperback
ISBN	1470470462 paperback
ISBN	electronic book

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Self-similar and self-affine sets and measures / Balázs Bárány, Károly Simon, Boris Solomyak.

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