Abstract:One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to characterize such systems we define a property called "multichaos". A set X is multi-chaotic if X has a dense trajectory and for at least 2 values of k, the k-dimensionally unstable periodic points are dense in X. All proofs that such a behavior holds have been based on hyperbolicit… Show more
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