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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Cryptanalysis of a new chaotic cryptosystem based on ergodicity
TL;DR: In this article, the security of a recent cryptosystem based on the ergodicity property of chaotic maps is analyzed, and it is shown how to obtain the secret key using a chosen-ciphertext attack.
Journal ArticleDOI
Preturbulent states and renormalization group for simple models
C. Tresser,P. Coullet +1 more
TL;DR: In this article, some one-parameter first-order difference-equations of the form X i + 1 = f (R,X i ), arising in theoretical biology and now used as simple models for turbulent behavior, are studied.
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Statistical versus optimal partitioning for block entropies
TL;DR: An algorithm is provided to provide a simple answer (an algorithm), although approximative, in connection with symbolic dynamics and statistical properties of 1‐d maps on the interval in relation to the logistic map.
Book ChapterDOI
Instabilities and Chaos in a Chemical Reaction
TL;DR: In this article, phase space portraits, Poincare sections, and maps have been obtained from experiments on the Belousov-Zhabotinskii chemical reaction and the dynamical behavior is described by a strange attractor, that is, the largest Lyapunov exponent is positive.
Journal ArticleDOI
Decomposition of Necklaces
William Y. C. Chen,Jun Wang +1 more
TL;DR: In this article, a branching property of primitive self-complementary necklaces is presented, leading to a combinatorial explanation of an analogous property of MSS sequences.
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
Journal ArticleDOI