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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A note on chaotic unimodal maps and applications.
TL;DR: By stabilizing unstable periodic orbits on superstable periodic orbits, this work develops techniques to control the generation of long binary sequences andoretical and numerical evidence that the set of the maximum-length shift-register sequences is a subset of the sets of one-dimensional chaotic unimodal maps.
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Bifurcation Structures in a Bimodal Piecewise Linear Map
TL;DR: An overview of the results concerning dynamics of a piecewise linear bimodal map is presented and a family of regions closely related to the so-called U-sequence is described.
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Some Number Theoretical Aspects on Periodic Orbits of a Tent Map
TL;DR: Some number theoretical aspects on periodic orbits of a one-dimensional dynamical system x"n"+"1 = @?(x"n) are presented in this paper.
ReportDOI
Chaos and related nonlinear noise phenomena in Josephson tunnel junctions
TL;DR: The nonlinear dynamics of Josephson tunnel junctions shunted by a resistance with substantial self-inductance have been thoroughly investigated in this paper, and it has been shown that very large increases in low-frequency voltage noise with equivalent noise temperatures of 10/sup 6/ K or more, observed in the vicinity of these regions, arise from switching, or hopping, between subharmonic modes.
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Coding Rule for Periodic Orbits in the One-dimensional Map
TL;DR: In this article, a new coding rule for periodic orbits in unimodal one-dimensional maps is derived, where the band merging is observed in the bifurcation diagram of the logistic map.
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