Self-similar groups
By: Volodymyr Nekrashevych
Series: Mathematical surveys and monographs -- v. 117; Mathematical surveys and monographs -- no. 117
Publisher: American Mathematical Society
Published: 2005
Place of publication: Providence, R.I
Language: eng
Number of pages: 231
Subjects: Geometric group theory; Symbolic dynamics; Self-similar processes
Description: "The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book." "A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible, to a wide mathematical readership, including graduate students interested in group theory and dynamical systems."--BOOK JACKET.
Notes: Includes bibliographical references (p. 223-228) and index