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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Cryptanalysis of a family of self-synchronizing chaotic stream ciphers
TL;DR: In the present work a thorough analysis of the keystream is made which reveals the existence of some serious security problems of the proposed stream cipher.
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Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems
Nickolay Korabel,Rainer Klages +1 more
TL;DR: A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map and it is found that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter.
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Non-equilibrium behaviour in isothermal liquid chemical systems
C. Vidal,P. Hanusse +1 more
TL;DR: The main features, goals, and achievements of a field of research that is now commonly referred to as "Chemical Dynamics" are reviewed in this article, which is neither molecular dynamics nor chemical kinetics, in the traditional sense, but rather the study of the universal properties of time evolution and/or spatial structure of chemical systems evolving far from equilibrium.
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Chaos in a solid-state laser with a periodically modulated pump
TL;DR: A NdP(5)O(14) laser at 1.325-microm wavelength pumped by an Ar(+) laser whose intensity is periodically modulated at a rate comparable with the relaxation-oscillation frequency shows a period-doubling sequence, chaotic emission, and windows of regular pulsing within the chaotic region.
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Oscillatory modes in a nonlinear second-order differential equation with delay
TL;DR: In this article, the second-order delay-differential equation x(t)=−ax(t)+f[x(t−Τ)] is studied wheref is a piecewise constant function which mimics negative feedback.
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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