A Tale of Two Fractals

Authors: Kirillov, A.A.

  • First book to provide a rigorous study of fractals usable by undergraduates
  • Written by a renowned authority in the field and expert at communicating mathematical ideas to students
  • An excellent means for young mathematicians to acquire basic tools from many different areas
  • Abundant figures and exercises provide valuable clarity and practice
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eBook $29.99
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  • ISBN 978-0-8176-8382-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $39.95
price for USA
  • ISBN 978-0-8176-8381-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
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About this Textbook

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the 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 by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a 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 other areas.

Reviews

From the reviews:

“A Tale of Two Fractals was intended to bridge the gap between popular expositions on fractals and peer-reviewed 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.” (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 Sierpiński 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.” (Vicenţiu D. Rădulescu, zbMATH, Vol. 1273, 2013)


Table of contents (8 chapters)

  • Definitions and General Properties

    Kirillov, A. A.

    Pages 3-17

  • The Laplace Operator on the Sierpiński Gasket

    Kirillov, A. A.

    Pages 19-27

  • Harmonic Functions on the Sierpiński Gasket

    Kirillov, A. A.

    Pages 29-54

  • Circles and Disks on Spheres

    Kirillov, A. A.

    Pages 57-78

  • Definition of the Apollonian Gasket

    Kirillov, A. A.

    Pages 79-94

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-0-8176-8382-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $39.95
price for USA
  • ISBN 978-0-8176-8381-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Tale of Two Fractals
Authors
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8382-5
DOI
10.1007/978-0-8176-8382-5
Hardcover ISBN
978-0-8176-8381-8
Edition Number
1
Number of Pages
XIII, 138
Topics