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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External arguments for the chaotic bands calculation in the Mandelbrot set
TL;DR: In this article, the chaotic bands of any Mandelbrot set hyperbolic component were analyzed using external arguments in order to identify the hyper-bolic components, and the harmonics of the external arguments were used as a tool to calculate chaotic bands.
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Response of an acousto-optic device with feedback to time-varying inputs
TL;DR: It is found that novel changes of the output period can occur for significant feedback amplitudes, and that these changes can be sensitively controlled.
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Further results on periods and period doubling for iterates of the trapezoid function
W. A. Beyer,P. R. Stein +1 more
TL;DR: In this paper, the trapezoidal function @lf"e(x) is defined for fixed e @? (0, 1) and for fixed l @? [1, 2] for bifurcation diagrams.
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Metric properties of non-renormalizable S-unimodal maps: II. Quasisymmetric conjugacy classes
Michael Jakobson,G. Świạtek +1 more
TL;DR: In this paper, it was shown that for certain classes of S-unimodal maps with aperiodic kneading sequences, the topological conjugacies are also quasisymmetric.
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Counting the number of periods in one-dimensional maps with multiple critical-points
Fa-geng Xie,Bailin Hao +1 more
TL;DR: The problem of counting the number of different periodic orbits in continuous maps of an interval is solved in this paper, where the authors give tabulated values for Nm(n) for m = 2 to 7.
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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