On finite limit sets for transformations on the unit interval
TLDR
An infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself and the structure and order of occurrence is universal for the class.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-07-01 and is currently open access. It has received 521 citations till now. The article focuses on the topics: Limit superior and limit inferior & Limit (mathematics).read more
Citations
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Evolution of a multimodal map induced by an equivariant vector field
TL;DR: In this article, the authors consider the case when the equivariance of the studied system is taken into account to study the evolution of the population of periodic orbits when a control parameter is varied.
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Time Quasilattices in Dissipative Dynamical Systems
Felix Flicker,Felix Flicker +1 more
TL;DR: In this article, the existence of time quasilattices as stable trajectories in dissipative dynamical systems was established, and it was shown that the infinite Pell and Clapeyron words of increasing length provide systematic periodic approximations to time quaïrstices which can be verified experimentally.
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Cryptanalysis of a new chaotic cryptosystem based on ergodicity
TL;DR: This paper analyzes the security of a recent cryptosystem based on the ergodicity property of chaotic maps and shows how to obtain the secret key using a chosen-ciphertext attack.
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Is the Universe a Universal Computer
TL;DR: In this paper, Wolfram argues that the best way to understand many systems in nature is to think in terms of simple programs instead of mathematical equations, and he argues that this is the case even in the case of artificial intelligence.
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Symbolic dynamics. I. Finite dispersive billiards
TL;DR: In this article, it was shown that forbidden and allowed orbits are separated by a monotone pruning front, which can be approximated by a sequence of finite symbolic dynamics grammars.
References
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Book
Non-linear transformation studies on electronic computers
P. R. Stein,Stanisław Ulam +1 more
TL;DR: In this paper, the properties of non-linear transformations in Euclidean spaces are examined, and the invariant points, finite sets, and invariant subsets of the transformations and the means for obtaining them constructively are considered.
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Eine Bemerkung über die Gruppe der topologischen Abbildungen der Kreislinie auf sich selbst
Józef Schreier,Stanislaw M. Ulam +1 more
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