Exploring chaotic motion through periodic orbits (original) (raw)

Physical Review Letters, 1987

Abstract

2388 7, 1, 15, 29, 63, 55, 103, respectively. The Lyapunov numbers of all these cycles were calculated. To check the validity and accuracy of our algorithms we compared the results with" exact" calculations which use the explicit knowledge of the map.(In extracting the data from the chaotic signal as above no knowledge of the underlying map is assumed.) In this calculation one first lays a grid of points covering the attractor. Typically the num-ber of grid points is at least 5 timeslarger than the num-ber of periodic points that one expects to find. ...

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