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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Symbolic approach to intermittency
TL;DR: In this paper, the use of the MSS universal sequences in numerical and experimental studies of type I intermittency was proposed, which can be easily measured and provide a reliable and unambiguous way of testing intermitency scaling laws and the predictions of one-dimensional maps.
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Influence of asymmetries on N-tupling sequences
TL;DR: In this paper, it was shown that the metric universality associated with the N -tupling sequences of a symmetric S-unimodal map is completely changed when an asymmetry is introduced at the maximum of the map.
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Superconvergence of topological entropy in the symbolic dynamics of substitution sequences
Leon Zaporski,Felix Flicker +1 more
TL;DR: In this article, the authors consider infinite sequences of superstable orbits (cascades) generated by systematic substitutions of letters in the symbolic dynamics of one-dimensional nonlinear systems in the logistic map universality class.
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Construction of Poincaré maps for multiply periodic and chaotic flows
TL;DR: In this paper, a method is described for the construction of approximate analytical Poincare maps from next amplitude plots of three-dimensional differential equation systems, which are computed in the coordinate space and parameter space of the differential equations.
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Chaos in a Model of Credit Cycles with Good and Bad Projects.
TL;DR: In this article, the authors consider a credit cycle model defined by a one-dimensional piecewise smooth map with upward, downward and flat branches and obtain conditions of abrupt transition from an attracting fixed point to an attracting cycle or chaotic attractor (cyclic chaotic intervals).
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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