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Tr. Mat. Inst. Steklova, 2000, Volume 231, Pages 134–214 (Mi tm515)  

This article is cited in 143 scientific papers (total in 144 papers)

Automata, Dynamical Systems, and Groups

R. I. Grigorchuk, V. V. Nekrashevych, V. I. Sushchanskii

Abstract: This paper is devoted to the groups of finite automata and their applications in algebra, dynamical systems, and geometry. The groups of synchronous automata as well as the groups of asynchronous automata are considered. The problems of reduction of finite asynchronous automata, the types of growth of finite synchronous automata, and the conditions of embeddability of groups in the group of automata are studied. The automorphism groups of cellular automata are investigated. A group of rational homeomorphisms of the Cantor set is introduced. The dynamics, on the boundary of a tree, determined by an automaton group is investigated. Certain unsolved problems are formulated.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 231, 128–203

Bibliographic databases:
UDC: 515.164.63
Received in May 2000

Citation: R. I. Grigorchuk, V. V. Nekrashevych, V. I. Sushchanskii, “Automata, Dynamical Systems, and Groups”, Dynamical systems, automata, and infinite groups, Collected papers, Tr. Mat. Inst. Steklova, 231, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 134–214; Proc. Steklov Inst. Math., 231 (2000), 128–203

Citation in format AMSBIB
\by R.~I.~Grigorchuk, V.~V.~Nekrashevych, V.~I.~Sushchanskii
\paper Automata, Dynamical Systems, and Groups
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 134--214
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 128--203

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