Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.1, pp.81--86

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 1, pp.81--86

The Turning Point Dynamics and the Organization of Chaos in Iterative Maps.
F.K. Diakonos and P. Schmelcher

We study the dynamics of one dimensional iterative maps in the regime of fully developed chaos. Introducing the concept of the turning points we extract from the chaotic trajectories the corresponding turning point trajectories which represent a strongly correlated part of the chaotic dynamics of the system. The density of turning points exhibits step like structures at the positions of the unstable fix points. The turning point dynamics is discussed and the corresponding turning point map, which possesses an appealing asymptotic scaling property, is investigated. As a first application of the turning point concept we demonstrate its usefulness for the analysis of time series and provide an algorithm, which allows to locate the fixed points in one dimensional time series.
Key words: chaotic dynamics, iterative maps, asymptotic scaling property.

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