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A new test for chaos in deterministic systems
We describe a new test for determining whether a given deterministic dynamical system is chaotic or non–chaotic. In contrast to the usual method of computing the maximal Lyapunov exponent, our methodExpand
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On the Implementation of the 0-1 Test for Chaos
TLDR
In this paper we address practical aspects of the implementation of the 0–1 test for chaos in deterministic systems. Expand
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Asymptotic stability of heteroclinic cycles in systems with symmetry. II
Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into theExpand
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An example of a non-asymptotically stable attractor
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Testing for Chaos in Deterministic Systems with Noise
Abstract Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditionalExpand
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Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered byExpand
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A vector-valued almost sure invariance principle for hyperbolic dynamical systems
We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. TheseExpand
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Large deviations for nonuniformly hyperbolic systems
We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decayExpand
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The Lorenz Attractor is Mixing
We study a class of geometric Lorenz flows, introduced independently by Afraimovič, Bykov & Sil′nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. As aExpand
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Large and moderate deviations for slowly mixing dynamical systems
We obtain results on large deviations for a large class of nonuniformly hyperbolic dynamical systems with polynomial decay of correlations , . This includes systems modelled by Young towers withExpand
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