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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Book ChapterDOI
Properties of continuous maps of the interval to itself
P. Collet,J. P. Eckman +1 more
Journal ArticleDOI
Scaling factors associated withM-furcations of the 1−μ∥x∥z map
TL;DR: In this paper, a numerical study of the scaling behavior associated with M-furcations (M=3, 4, 5) in the map is made, where scaling constants δ and α are calculated as functions ofz, as well as the more general scaling functions α and f(a).
Journal ArticleDOI
Coupled logistic maps in physico-chemical processes: coexisting attractors and their implications
TL;DR: In this paper, multiply periodic stable solutions have been found numerically for a coupled logistic map with symmetric coupling and the evolution towards chaos of the period 6 attractor, as well as the basins of attraction in the space of the initial conditions, have been studied.
OtherDOI
Self-Generated Chaotic Behavior in Nonlinear Mechanics §
TL;DR: The phase space of most Hamiltonian and many Dissipative systems is dotted with chaotic regions in which some properties of many orbits are as random as coin tosses, even though the system is deterministic.
Journal ArticleDOI
An algebraic measure of complexity
TL;DR: In this paper, a reading operator is introduced to determine what are the state aspects that are observable, and the set of configurations is ordered in complexity layers, defined as classes of configurations that are stabilized by isomorphic subgroups of (σ), up to an isomorphism, stabilizing the configurations in a given layer.
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.
Journal ArticleDOI
Eine Bemerkung über die Gruppe der topologischen Abbildungen der Kreislinie auf sich selbst
Józef Schreier,Stanislaw M. Ulam +1 more
Journal ArticleDOI