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Tale of two fractals / A.A. Kirillov.

By: Material type: TextTextPublication details: New York : Springer, 2013.Description: xiii, 138 p. : illustrations (some color) ; 24 cmISBN:
  • 9780817683818
Subject(s): DDC classification:
  • 23 K58 514.742
Contents:
1. Definitions and general properties -- 2. The Laplace operator on the Sierpiński gasket -- 3. Harmonic functions on the Sierpiński gasket -- 4. Circles and disks on spheres -- 5. Definition of the Apollonian gasket -- 6. Arithmetic properties of Apollonian gaskets -- 7. Geometric and group-theoretic approach -- 8. Multidimensional Apollonian gaskets-- Bibliography-- Index.
Summary: Written by the 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 theory of fractals.
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Includes bibliographical references and index.

1. Definitions and general properties --
2. The Laplace operator on the Sierpiński gasket --
3. Harmonic functions on the Sierpiński gasket --
4. Circles and disks on spheres --
5. Definition of the Apollonian gasket --
6. Arithmetic properties of Apollonian gaskets --
7. Geometric and group-theoretic approach --
8. Multidimensional Apollonian gaskets--
Bibliography--
Index.

Written by the 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 theory of fractals.

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