Edward Ott

TL;DR: In this paper, the authors consider embeddings with self-intersection and show that reliable prediction is still possible from most orbit points when the dimension M of the measurement space exceeds the information dimension D{sub 1} of the attractor.

TL;DR: A method is proposed whereby the full state vector of a chaotic system can be reconstructed and tracked using only the time series of a single observed scalar function of the system state.

TL;DR: In this article, the authors studied the properties of scars on eigenfunctions of a two-dimensional, classically chaotic billiard and showed that the tendency for a scar to form is controlled by both the stability of the periodic orbit and the statistical fluctuations in the time for wave density to return to the unstable orbit once having left.

TL;DR: In this article, the nonlinear interaction of two coherent waves with particles of velocity near (ω 1−ω 2) and (k 1−k2) was investigated. But the results were only applicable to the case of (1 − ε)-coherence.

TL;DR: In this paper, an adaptive strategy that, based on a potential that the network systems seek to minimize in order to maintain synchronization, can be successfully applied to identify the time evolution of the network from limited information, taking advantage of the properties of synchronism of chaos and the presence of different communication delays over the network links.