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A TALE OF TWO FRACTALS

A.a. Kirillov

Oprawa:
TWARDA

Wydawca:
Springer New York

ISBN:
9780817683818

327,55 PLN
Wysyłamy w 28 dni

Opis produktu

Since Benoit Mandelbrots pioneering work in the late 1970s scores of researcharticles and books have beenpublished on the topic of fractals.Despite thevolume of literature in the fieldthe general level of theoretical understanding has remained low: most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use.Written bycelebrated mathematician and educator A.A. Kirillov A Tale of Two Fractals/ is intended to helpbridge this gap providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The workis designed to give young nonspecialist mathematiciansa solid foundation in the theory of fractals and in the process to equip them with exposure to a variety of geometric analytical and algebraic tools with applications across otherWritten bythe celebrated mathematician and educator A.A. Kirillov this book offers an original treatment of fractals that is accessible to beginners and sufficiently rigorous for serious mathematicians. Offers a solid foundation in the theIntroduction. Part 1. The Sierpiski Gasket. Definition and General Properties. The Laplace Operator on the Sierpiski Gasket.Harmonic Functions on the Sierpiski Gasket. Part 2. The Apollonian Gasket. Introduction. Circles and Disks on Spheres. Definition of the Apollonian Gasket. Arithmetic Properties of Apollonian Gaskets. Geometric and GroupTheoretic Approach. ManyDimensional Apollonian GasketsFrom the reviews:/A Tale of Two Fractals was intended to bridge the gap between popular expositions on fractals and peerreviewed research papers. Kirillov (Univ. of Pennsylvania) includes open questions and conjectures along with references to papers and books that expand upon particular topics beyond the scope of the present volume. the book is a useful addition to libraries supporting graduate programs in mathematics . Summing Up: Recommended. Graduate students and above.Ł (C. Bauer Choice Vol. 51 (4) December 2013)/This volume deals with several mathematical problems concerning the qualitative analysis of some models on fractal domains. The author is mainly concerned with the Sierpiski and Apollonian gaskets. This volume contains important advances in the theory of fractal sets or hyperbolic geometry. The book is a valuable resource for graduate students and researchers in applied nonlinear analysis.Ł (Viceniu D. Rdulescu zbMATH Vol. 1273Since Benoit Mandelbrots pioneering work in the late 1970s scores of researcharticles and books have beenpublished on the topic of fractals. Despite thevolume of literature in the fieldthe general level of theoretical understanding has remained low: most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use.Written bycelebrated mathematician and educator A.A. Kirillov

Wymiary: 3554 gr 155 mm 235 mm

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