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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Long tailed maps as a representation of mixed mode oscillatory systems
TL;DR: In this article, the scaling relation of the dominant windows of periodic orbits sandwiched between two successive states of RLk sequence is derived for a family of two-dimensional Poincare maps with a unique critical point.
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Universality of the fine structure in the chaotic regime of one-dimensional maps
TL;DR: In this paper, the periodic windows in the chaotic regime of three one-dimensional maps are arranged in a symbolic binary tree and by their period respectively, and the scaling properties of the measure of these windows are studied numerically.
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Chaos in modulated logistic systems
TL;DR: A review of the work done on the dynamics of modulated logistic systems can be found in this article, where three different problems are treated: the modulated map, the parametrically perturbed logistic map and the combination map obtained by combining two maps of the quadratic family.
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A new scaling along the spike of the Mandelbrot set
TL;DR: Using the zeros of a family of real polynomials, a sequence of midgets are located along the spike of the Mandelbrot set and evidence supporting a pattern of scalings for some “generalized Mandel Brot sets” is presented.
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On the universality class dependence of period doubling indices
Mario Feingold,Diego L. González,Marcelo O. Magnasco,Marcelo O. Magnasco,Oreste Piro,Oreste Piro,Oreste Piro +6 more
TL;DR: In this article, the dependence on ν of the period doubling scaling indices for unimodal maps with a critical point of the form |x|ν is numerically investigated.
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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