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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Monotonicity of entropy for real multimodal maps
Henk Bruin,Sebastian van Strien +1 more
TL;DR: In this paper, it was shown that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected.
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Devil's attractors and chaos of a driven impact oscillator
TL;DR: In this paper, the motion of a driven elastic impact oscillator, where x + 0.4 x + x = cos (ωt), x > 0 and x (t + ) = - x t − ) at x = 0, is studied for ω ≈ 2−4.
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Dynamics of a close-loop controlled MEMS resonator
TL;DR: In this article, the dynamics of a close-loop electrostatic MEMS resonator, proposed as a platform for ultra sensitive mass sensors, is investigated to determine the optimal operating regions.
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Chaotic and Periodic Potential Oscillations in Formaldehyde Oxidation
TL;DR: In this paper, the appearance of chaos and windows of periodic oscillations in the galvanostatic oxidation of formaldehyde on platinum at 43 °C was studied using various applied currents and formaldehyde concentrations.
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Continuous itinerary functions and dendrite maps
TL;DR: In this article, the authors examined the kneading sequence theory of maps on dendrites, concentrating on those maps having one "turning point" and the unique itinerary property (i.e., distinct points have distinct itineraries).
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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