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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Periodic orbits near onset of chaos in plane Couette flow.
Tobias Kreilos,Bruno Eckhardt +1 more
TL;DR: A symbolic dynamics for the orbits is introduced and it is shown that the ones that exist fall into the universal sequence described by Metropolis, Stein and Stein for unimodal maps.
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Universal metric properties of bifurcations of endomorphisms
TL;DR: In this article, it is shown how this problem is similar to the renormalisation problem, and how the bifurcation velocity may be derived from a fixed-point theory.
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Computational synergetics and mathematical innovation
TL;DR: In this article, it is demonstrated how the computer, used in a heuristic mode, has greatly augmented our understanding of the mathematics of nonlinear dynamical process, and the role of good graphics in enhancing the discovery and retention of new mathematical properties of equations is illustrated.
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Two-parameter study of the routes to chaos
TL;DR: In this article, the authors studied the routes to chaos for a Rayleigh-Benard experiment in mercury, as a function of two parameters, the Rayleigh number (R ) and the Chandrasekhar number (Q ).
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Introduction to real-space renormalization-group methods in critical and chaotic phenomena
TL;DR: In this article, a survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given.
References
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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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