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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Changing criteria for imposing order
TL;DR: The origins, the early development, and some recent trends in the study of chaos are reviewed and new methods of non-linear dynamics may be used to infer the underlying order in ‘noisy’ ecological and epidemiological time series.
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Universality, multiplicity, and the effect of iron impurities in the Belousov–Zhabotinskii reaction
K. G. Coffman,K. G. Coffman,William D. McCormick,Zoltán Noszticzius,Reuben H. Simoyi,Reuben H. Simoyi,Harry L. Swinney +6 more
TL;DR: In this article, a sequence of period doubling bifurcations was observed as a parameter was varied, and beyond the accumulation point for the period doubling sequence there was a sequence with the same symbolic dynamics as the states of the U (universal) sequence of Metropolis, Stein, and Stein (1973).
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Relative Rotation Rates for Driven Dynamical Systems
Hernán G. Solari,Robert Gilmore +1 more
TL;DR: In this paper, a topological classification of nonlinear dynamical systems with a single forcing frequency is presented. But the results presented in this paper represent a first step in an attempt to construct a topology classification for nonlinear systems.
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Universal bifurcations and the classification of cardiac arrhythmias.
TL;DR: It is shown that mathematics can provide a framework for studying several cardiac arrhythmias and that it is possible to theoretically predict dynamics in some biological models and clinical situations using appropriate mathematical models.
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Bifurcations in a model of magnetoconvection
Edgar Knobloch,Nigel Weiss +1 more
TL;DR: In this article, the authors studied the bifurcations from oscillatory solutions in a truncated model of two-dimensional Boussinesq magnetoconvection, where the fifth order system of nonlinear differential equations is integrated numerically and in certain parameter regimes there is a bifurbcation from symmetrical to asymmetrical oscillations followed by a period-doubling cascade.
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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