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

Trudy Matematicheskogo Instituta imeni V.A. Steklova

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2000, Volume 231, Pages 134–214 (Mi tm515)

This article is cited in 177 scientific papers (total in 178 papers)

Automata, Dynamical Systems, and Groups

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

Full-text PDF (880 kB) Citations (178)

References:

PDF

HTML

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.

Received in May 2000

Bibliographic databases:

Document Type: Article

UDC: 515.164.63

Language: Russian

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

Citation in format AMSBIB

\Bibitem{GriNekSus00}

\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 Trudy Mat. Inst. Steklova

\yr 2000

\vol 231

\pages 134--214

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm515}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1841755}

\zmath{https://zbmath.org/?q=an:1155.37311}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2000

\vol 231

\pages 128--203

Linking options:

https://www.mathnet.ru/eng/tm515

https://www.mathnet.ru/eng/tm/v231/p134

This publication is cited in the following 178 articles:

A. V. Zharkova, “Kolichestvo attraktorov i tsiklicheskikh sostoyanii v konechnykh dinamicheskikh sistemakh orientatsii polnykh grafov”, PDM, 2024, no. 63, 91–101
N. V. Muravev, “Maximal finite orders of linear automata over arbitrary field”, Moscow University Mathematics Bulletin, 79:5 (2024), 262–264
Oliynyk A.S., Prokhorchuk V.A., “Amalgamated Free Product in Terms of Automata Constructions”, Commun. Algebr., 50:2 (2022), 740–750
Aroca J., Bleak C., “Some Embeddings Between Symmetric R. Thompson Groups”, Proc. Edinb. Math. Soc., 65:1 (2022), 1–18
Rump W., “Self-Similar Monoids Related to Hahn Groups”, Semigr. Forum, 104:2 (2022), 448–463
Brothier A., “Classification of Thompson Related Groups Arising From Jones Technology i”, Int. Math. Res. Notices, 2022
N. V. Muravev, “Order estimates of linear automata”, Moscow University Mathematics Bulletin, 77:6 (2022), 262–268
R. I. Grigorchuk, P.-H. Leemann, T. V. Nagnibeda, “Finitely generated subgroups of branch groups and subdirect products of just infinite groups”, Izv. Math., 85:6 (2021), 1128–1145
Olukoya F., “Automorphism Towers of Groups of Homeomorphisms of Cantor Space”, Isr. J. Math., 244:2 (2021), 883–899
Bondarenko I., Waechter J.Ph., “On Orbits and the Finiteness of Bounded Automaton Groups”, Int. J. Algebr. Comput., 31:06 (2021), 1177–1190
Nagnibeda T. Perez A., “Schreier Graphs of Spinal Groups”, Int. J. Algebr. Comput., 31:06 (2021), 1191–1216
Bleak C., Cameron P.J., Olukoya F., “Automorphisms of Shift Spaces and the Higman-Thompson Groups: the One-Sided Case”, Discrete Anal., 2021
Broise-Alamichel A., Parkkonen J., Paulin F., “Rate of Mixing For Equilibrium States in Negative Curvature and Trees”, Thermodynamic Formalism, Lect. Notes Math., Lecture Notes in Mathematics, 2290, eds. Pollicott M., Vaienti S., Springer International Publishing Ag, 2021, 291–315
Bezuglyi I S., Sanadhya Sh., “Cohomology of Hyperfinite Borel Actions”, Group. Geom. Dyn., 15:4 (2021), 1363–1398
Grigorchuk R. Simanek B., “Spectra of Cayley Graphs of the Lamplighter Group and Random Schrodinger Operators”, Trans. Am. Math. Soc., 374:4 (2021), 2421–2445
Steinberg B., Szakacs N., “Simplicity of Inverse Semigroup and Etale Groupoid Algebras”, Adv. Math., 380 (2021), 107611
Prokhorchuk V., “Generation of Amalgamated Free Products of Cyclic Groups By Finite Automata Over Minimal Alphabet”, Theor. Comput. Sci., 856 (2021), 151–164
Grigorchuk R. Samarakoon S., “Integrable and Chaotic Systems Associated With Fractal Groups”, Entropy, 23:2 (2021), 237
Cavaleri M., D'Angeli D., Donno A., Rodaro E., “Graph Automaton Groups”, Adv. Group Theory Appl., 11 (2021), 75–112
Belk J., Bleak C., Matucci F., “Rational Embeddings of Hyperbolic Groups”, J. Comb. Algebra, 5:2 (2021), 123–183

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

Statistics & downloads:
Abstract page:	4033
Full-text PDF :	1695
References:	189
First page:	5

Что такое QR-код?

Registration to the website

Logotypes