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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Characterizing Cantorian sets by entropy‐like quantities
TL;DR: This paper derives a new diagnostic for Cantorian stochastic automata, which could find a direct application to biology, where there is a recent claim that the coding regions of chromosomes form Cantor sets.
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University of Succession of Periodic Windows in Families of 1-D Maps
TL;DR: In this paper, the authors discuss the universality of succession of periodic windows for a broad class of families of maps of the unit interval using the notion of a critical iterate.
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Conjugation of cascades
TL;DR: In this article, it was shown that all the saddle-node bifurcation cascades associated with every last appearance p-periodic orbit (p = 3, 4, 5, … ) can also be generated from the very Feigenbaum cascade.
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Misiurewicz point patterns generation in one-dimensional quadratic maps
TL;DR: In this paper, the authors study the patterns of the symbolic sequences of both Misiurewicz and superstable periodic points, and show that a misiurewichz point pattern can be obtained as the limit of the sum of a superstability periodic orbit pattern plus itself or some of its heredity transmitters repeated an infinite number of times.
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Chaos in phase-conjugate resonators as a multimodal mapping
Milivoj R. Belić,Predrag Stojkov +1 more
TL;DR: In this article, an optical phase-conjugate resonator, realized by a Kerr-like phase conjugator, represented by a two-dimensional slowly varying envelope plane-wave model is driven to chaos using two laser pumps in standard four-wave mixing geometry.
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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