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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Harmonic Analysis in Discrete Dynamical Systems
TL;DR: In this article, a review of 1D and 2D quadratic maps is presented, with a focus on the applications in discrete dynamical systems and pseudoharmonics and pseudoantiharmonics.
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General form of superuniversality for fractal dimensions in one-dimensional maps
TL;DR: In this article, a superuniversal relationship between scaling factors alpha(e) and fractal dimensions d of Feigenbaum-type attractors on all critical (accumulation) points of transitions to chaos is established.
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Transient Dynamics Inside Periodic Windows and in Their Vicinity I. Logistic Maps
TL;DR: Property of dynamics in terms of rambling time inside periodic windows and duration of the non-laminar phase in their proximity are studied, showing that a close relation between these two notions exists.
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The many facets of Poincare recurrence theorem of the logistic map
TL;DR: This paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map, in different tests and computations, each one illuminating the many aspect of the problem of recurrence.
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Universal visibility patterns of unimodal maps
TL;DR: In this article, the authors apply horizontal visibility to study the class of unimodal maps that give rise to equivalent bifurcation diagrams and show that there are visibility patterns in each cascade of the logistic diagram, converging at the onset of chaos.
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