Last edited by Mikakazahn
Tuesday, May 5, 2020 | History

5 edition of Self-similar groups found in the catalog.

Self-similar groups

by Volodymyr Nekrashevych

  • 309 Want to read
  • 8 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Geometric group theory,
  • Symbolic dynamics,
  • Self-similar processes

  • Edition Notes

    Includes bibliographical references (p. 223-228) and index

    StatementVolodymyr Nekrashevych
    SeriesMathematical surveys and monographs -- v. 117, Mathematical surveys and monographs -- no. 117
    Classifications
    LC ClassificationsQA183 .N45 2005
    The Physical Object
    Paginationxi, 231 p. :
    Number of Pages231
    ID Numbers
    Open LibraryOL15534448M
    ISBN 100821838318
    LC Control Number2005048021

    Schreier graphs of self-similar actions of groups have been largely studied from the viewpoint of spectral computations, growth, amenability and topology of Julia sets,,,,,,. It is shown in that the graph X 0 ∞ is isomorphic to the Schreier graph of the infinite word 0 ∞ under the action of the group G. We generalize this analysis by Cited by: A fundamental class of groups acting on T q is the class of self-similar groups. A group Gacting on T q is self-similar if, for any g∈ Gand x∈ X, there exist h∈ Gand y∈ Xsuch that g(xw) = yh(w), for all w∈ X∗. Self-similarity was related in most cases with geometrical objects and only recently the File Size: KB.

    Self-similar solutions Self-similarities of the second kind: first examples Self-similarities of the second kind: further examples Classification of similarity rules and self-similarity solutions. Recipe for application of similarity analysis Scaling and transformation groups. Renormalization groups. 7. Post-critically finite self-similar groups, Algebra and Discrete Mathematics, 2, no 4, () pp. , (with Evgen Bondarenko). Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms, Groups: Topological, Combinatorial and Arithmetic Aspects, T.W. Müller, editor, volume of LMS Lecture Notes Series.

    A Sampling of Remarkable Groups: Thompson's, Self-similar, Lamplighter, and Baumslag-Solitar (Compact Textbooks in Mathematics) Marianna C. Bonanome. Paperback. A Book of Abstract Algebra: Second Edition Charles C. Pinter. out of 5 stars Kindle Edition. Wolfram Community forum discussion about The Delian Brick and other 3D self-similar dissections. Stay on top of important topics and build connections by joining .


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Self-similar groups by Volodymyr Nekrashevych Download PDF EPUB FB2

Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self Cited by: to describe self-similar actions of the free abelian groups Zn, making the relation between self-similar actions and numeration systems more explicit.

Section introduces the main class of self-similar actions for these notes. It is the class of the so-called contracting actions. An action is called contracting. Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc.

This book studies the self-similarity phenomenon in group theory and shows its relationship with dynamical systems. Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc.

This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self. Self-similar Groups by Nekrashevych, Volodymyr and a great selection of related books, art and collectibles available now at - Self-similar Groups Mathematical Surveys and Monographs by Volodymyr Nekrashevych - AbeBooks.

Abstract. Self-similar groups, or automata groups, consist of certain automorphisms of the infinite complete rooted binary tree. We describe them using several different concepts: computers are designed, portraits are drawn, and self-similar rules are : Marianna C.

Bonanome, Margaret H. Dean, Judith Putnam Dean. Groups covered include Thompson’s groups, self-similar groups, Lamplighter groups, and Baumslag-Solitar groups. Each chapter focuses on one of these groups, and begins by discussing why they are interesting, how they originated, and why they are important mathematically.

Self-similarity can be found in nature, as well. To the right is a mathematically generated, perfectly self-similar image of a fern, which bears a marked resemblance to natural plants, such as Romanesco broccoli, exhibit strong self-similarity.

In music. Strict canons display various types and amounts of self-similarity, as do sections of fugues. Citation: Rostislav Grigorchuk, Volodymyr Nekrashevych. Self-similar groups, operator algebras and Schur complement. Journal of Modern Dynamics,1 (3): Cited by: Introduction.

The name of the group comes from viewing the group as acting on a doubly infinite sequence of street lamps−, −,, each of which may be on or off, and a lamplighter standing at some lamp. An equivalent description for this, called the base group of is = ⨁ − ∞ ∞, an infinite direct sum of copies of the cyclic group where corresponds to a light that is off.

Self-similar groups. Here we review the basic definitions from theory of self-similar groups. For more see the paper [BGN03] and the book [Nek05].

Definition A self-similar group (G,X) is a group Gacting by automor-phisms on the rooted tree X∗ such that for every g∈ Gand every x∈ X there exist h∈ Gand y∈ X such that g(xw. The book explains the classification of a set of Walsh functions into distinct self-similar groups and subgroups, where the members of each subgroup possess distinct self-similar structures.

The observations on self-similarity presented provide valuable clues to tackling the inverse problem of. We show that the limits for dynamical systems of self-similar groups are eventually conjugate if, and only if, there is an isomorphism between their Deaconu groupoid preserving cocycles.

For limit solenoids of self-similar groups, we show that the conjugacy of limit solenoids is equivalent to existence of isomorphism between the Deaconu groupoids of limit solenoid preserving cocycles. \Self-similar groups and hyperbolic groupoids," minicourse of 4 lectures at Orl eans University, France \Self-similar and branch groups," minicourse of 3 lectures at \Group actions and dynamics," CRM, Montreal, Canada \Iterated monodromy groups," minicourse of 4 lectures at \Groups St Andrews in Bath," Bath, UK.

From self-similar structures to self-similar groups D. Kelleher1 B. Steinhurst2 *C.-M. Wong3 1Department of Mathematics University of Connecticut 2Department of Mathematics Cornell University 3Department of Mathematics Princeton University AMS Eastern Sectional Meeting, Fall Self-Similar Groups (Mathematical Surveys and Monographs) free ebook download: Views: 38 Likes: 2: Catalogue: Author(s): Volodymyr Nekrashevych: Date: Format: DJVU: Language: Those who downloaded this book also downloaded the following books: Comments.

New comment: (C) FreeBookSpot - Category: Mathematics. This is a survey paper on various topics concerning self-similar groups and branch groups with a focus on those notions and problems that are related to a 3-generated torsion 2 group of.

Our aim in this paper is to study the Ising model on the Schreier graphs of three key examples of self-similar groups: the first Grigorchuk's group of intermediate (i.e., strictly between. We prove that any subgroup of isometries of a Euclidean space can occur as a subgroup of isometries of a self-similar set.

Furthermore the isometry group of a planar self-similar set E satisfying the open set condition must be finite, and the possible groups of isometries are restricted by the cardinality of the system of similitudes that generates : Manuel Morán.

We explore the relationship between limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit space admits a self-similar structure, and also the condition such that this self-similar structure is p.c.f.

We then give the necessary and sufficient condition on a p.c.f. self-similar structure such that there Author: Daniel J. Kelleher, Benjamin A. Steinhurst, Chuen-Ming M. Wong. This, in essence, is the general idea behind clustering. We need a distance metric and a method to utilize that distance metric to find self-similar groups.

Clustering is a ubiquitous procedure in bioinformatics as well as any field that deals with high-dimensional data.Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity.

Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational.

The book begins from a non-traditional exposition of dimensional.Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group.

This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research Cited by: 7.