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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Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map
TL;DR: In this paper, the authors consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and decreasing branches, which are associated with a credit cycle model under the assumption of the Cobb-Douglas production function.
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Escape from the Unit Interval Under the Transformation x ↦λx(1 - x)
TL;DR: In this paper, it was shown that almost all of the unit interval eventually escapes if the transformation is iterated, and the question was raised for exactly what class of functions the theorem holds.
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Self-similarity of the bandcount adding structures: Calculation by map replacement
TL;DR: This work demonstrates that, using the map replacement approach, the bifurcation curves can be calculated much easier and confirms the hypothesis regarding the self-similarity of the bandcount adding structure.
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Universal scaling of generalized dimensions on critical strange sets
Ke-Fei Cao,Shou-Li Peng +1 more
TL;DR: In this paper, a scaling scheme of the generalized dimensions Dq(A)/D0(A) and the dimension spectra of singularities integral (alpha (q,A))/ integral ( alpha (0,A)), which is also universal, independent of all U-sequences A, is proposed.
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Application of Gray codes to the study of the theory of symbolic dynamics of unimodal maps
David Arroyo,Gonzalo Alvarez +1 more
TL;DR: The work described in this paper not only contributes to the integration of the different interpretations of symbolic dynamics of unimodal maps, it also points out some inaccuracies that exist in previous works.
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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