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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Journal ArticleDOI
Scaling and fine structure of superstable periodic orbits in the logistic map
J. Perrier,Frédéric Girault +1 more
TL;DR: In this paper , all superstable values of α are obtained numerically for period p up to 21, and the two smallest superstable parameters exhibit discrete fine structures, often different for even and odd p, combined with global and local scaling properties.
Journal ArticleDOI
Dissipative bifurcation ratio in the area-non-preserving Henon map
TL;DR: In this paper, the transition from periodic to chaotic behavior via a period doubling route is studied for dissipative systems and the bifurcation ratio which characterises such a transition is calculated for the area-non-preserving Henon map by using a simple renormalisation group method.
Book ChapterDOI
Multiplicity and Stability in Lumped-Parameter Systems (LPS)
M. Kubíček,M. Marek +1 more
TL;DR: Differentiation of dynamic systems into lumped-parameter systems (LPS) and distributed parameter systems (DPS) was discussed in Section 1.3. as discussed by the authors, where the phase space of LPS is a finite-dimensional space.
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Relation between Topological Entropies and Fractal Dimensions of Chaotic Attractors of the Hénon Map
TL;DR: In this article, the authors proposed an efficient approach for the estimation of topological entropies through the study on the integral relationship between fractal dimensions and topological Entropies.
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
Journal ArticleDOI