Book ChapterDOI
Subshifts behavior of cellular automata. topological properties and related languages
Gianpiero Cattaneo,Alberto Dennunzio +1 more
- Vol. 3354, pp 140-152
TLDR
This work describes the language related to a full transitive subshift extending the notion of irreducibility and shows how to associate to any subshift of finite type a cellular automaton which contains it.Abstract:
We study the subshift behavior of one dimensional cellular automata and we show how to associate to any subshift of finite type a cellular automaton which contains it. The relationships between some topological properties of subshifts and the behavior of the related languages are investigated. In particular we focus our attention to the notion of full transitivity. We characterize the language related to a full transitive subshift extending the notion of irreducibility.read more
Citations
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Journal ArticleDOI
An introduction to chaotic dynamical systems (2nd edition), by Robert L. Devaney. Pp 336. £34·95. 1989. ISBN 0-201-13046-7 (Addison-Wesley)
TL;DR: In this paper, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Journal ArticleDOI
A survey on transitivity in discrete time dynamical systems. application to symbolic systems and related languages
TL;DR: Transitivity (or some stronger versions of it) turns out to be the relevant condition of chaos and its role is discussed by a survey of some important results about it with the presentation of some new results.
Journal ArticleDOI
On the Behavior Characteristics of Cellular Automata
TL;DR: The inherent relationships between the running regulations and behavior characteristics of cellular automata are presented; an imprecise taxonomy of such systems is put forward; the three extreme cases of stable systems are discussed; and the illogicalness of evolutional strategies of cellular Automata is analyzed.
References
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Book
An introduction to chaotic dynamical systems
TL;DR: In this article, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Book
An Introduction to Ergodic Theory
TL;DR: The first part of the text as discussed by the authors provides an introduction to ergodic theory suitable for readers knowing basic measure theory, including recurrence properties, mixing properties, the Birkhoff Ergodic theorem, isomorphism, and entropy theory.
Book ChapterDOI
An Introduction to Ergodic Theory
TL;DR: Ergodic theory concerns with the study of the long-time behavior of a dynamical system as mentioned in this paper, and it is known as Birkhoff's ergodic theorem, which states that the time average exists and is equal to the space average.
Book
An Introduction to Symbolic Dynamics and Coding
Douglas Lind,Brian Marcus +1 more
TL;DR: Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises that explore symbolic dynamics as a method to study general dynamical systems.
Journal ArticleDOI
On Devaney's definition of chaos
TL;DR: In this paper, the definition of chaos is discussed and a discussion of Devaney's definition of Chaos is presented. But this discussion is limited to the case of chaos-constraints.