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Ergodic theory of chaos and strange attractors
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool theExpand
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Recurrence Plots of Dynamical Systems
A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.
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Iterated maps on the interval as dynamical systems
Motivation and Interpretation.- One-Parameter Families of Maps.- Typical Behavior for One Map.- Parameter Dependence.- Systematics of the Stable Periods.- On the Relative Frequency of Periodic andExpand
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A global attracting set for the Kuramoto-Sivashinsky equation
AbstractNew bounds are given for the L2-norm of the solution of the Kuramoto-Sivashinsky equation $$\partial _t U(x,t) = - (\partial _x^2 + \partial _x^4 )U(x,t) - U(x,t)\partial _x U(x,t)$$ , forExpand
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Entropy of dialogues creates coherent structures in e-mail traffic.
We study the dynamic network of e-mail traffic and find that it develops self-organized coherent structures similar to those appearing in many nonlinear dynamic systems. Expand
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Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
We show that values of the correlation dimension estimated over a decade from the Grassberger-Procaccia algorithm cannot exceed the value 2 log10N if N is the number of points in the time series.Expand
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Roads to turbulence in dissipative dynamical systems
Three scenarios leading to turbulence in theory and experiment are outlined. The respective mathematical theories are explained and compared.
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A computer-assisted proof of universality for area-preserving maps
I. Analysis of doubling: Feigenbaum universality for area-preserving maps Generating functions Further reduction of the problem Spectral properties Constructions of the operator $L$ Construction ofExpand
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The topological relationship between the large-scale attributes and local interaction patterns of complex networks
We show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. Expand
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Using Curvature and Markov Clustering in Graphs for Lexical Acquisition and Word Sense Discrimination
We introduce two different approaches for clustering semantically similar words. Expand
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