The Turning Point Dynamics and the Organization of Chaos in Iterative Maps
نویسندگان
چکیده
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.
منابع مشابه
A turning point analysis of the ergodic dynamics of iterative maps
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a turning point which represents a local minimum or maximum of the trajectory. Following we investigate the highly organized and structured distribution of turning ...
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