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
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Beyond Chaos
TL;DR: In this article, the authors define recursive interactions by means of logistic functions and derive a general result on the way interacting systems evolve in attractors, including single, irregular, folded, complex and discontinuous orbits.
Dissertation
Estimation of Chaos Function for the Implementation of High-Resolution Measurement System
TL;DR: Two different approaches have been proposed for the parameter estimation of the chaotic function tent map and it has been discovered that unique crossovers appear within the noisy samples and the information of the map fixed-point is preserved through the noisy dynamics of the TM.
Posted Content
Role of reinvestment in a competitive market
TL;DR: In this paper, the authors studied the asymptotic dynamics of a multi-dimensional piecewise smooth map which models an oligopoly market where competitors use adaptive scheme for reaction choice and each competitor also defines the moment for renewing the capital equipment depending on how intensively the latter is used.
Journal ArticleDOI
On Instability Leading to Chaos in Dynamical Systems
TL;DR: In this article, the stability conditions for the Chirikov-Taylor map are reviewed for a range of values of the non-linear parameter appearing in the map and the Strange attractor has also been discussed.
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Topological imprint for periodic orbits
TL;DR: In this article, the authors introduce the topological imprint to characterize crossing points and focus on the period-doubling cascade, which determines the topology imprint for orbits in chaotic bands.
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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