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
A neuro-diversified benchmark generator for black box optimization
Fengyang Sun,Lin Wang,Bo Yang +2 more
TL;DR: This study proposes a novel framework for randomly generating diversified benchmark functions to comprehensively evaluate evolutionary algorithms in a black box scenario and demonstrates a distinct difference among the performance of the tested optimizers on the proposed problems and the well-known CEC problems.
Journal ArticleDOI
Wielding intermittency with cycle expansions.
TL;DR: In this paper , the authors proposed a scheme to cooperate with cycle expansion and perturbation theory so that they can deal with intermittent systems and compute the averages more precisely, based on the integrability near the marginal orbits and the hyperbolicity in the part away from the singularities in intermittent systems.
Journal ArticleDOI
The invariant distribution of non-fully developed chaos for the tent map
TL;DR: In this article, the invariant distribution of non-fully developed chaos has been investigated for the tent map and a very sophisticated sequence set which corresponds to exact solutions of the invariants has been found, as a special case, the MSS (Metropolis-Stein Stein Stein) sequence is also included in this sequence set.
Book ChapterDOI
Bifurcation Structure in a Model of Monetary Dynamics with Two Kink Points
TL;DR: In this paper, the authors consider the discrete version of the Sargent & Wallace model with perfect foresight and obtain that the monetary dynamics are described by a one-dimensional map having two kink points, and show that when the slope of the money demand function is sufficiently large in absolute value and the speed of adjustment of the price to the market disequilibrium is smaller than 1 either cycles of any period or chaotic dynamics may be generated by the model.
Book ChapterDOI
Chaos and Noise
TL;DR: In this paper, the authors review methods for reconstructing a strange attractor from an observed signal if the underlying dynamics is chaotic, and the influence of external noise acting on chaotic systems is illustrated in some examples.
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