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Astronomical Time Series, Complexity in

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Abbreviations

Dynamical system:

A mathematical or physical system of which the evolution forward in time is determined by certain laws of motion – deterministic, random, or a combination.

Deterministic system:

A dynamical system the future of which, except for noise, can be exactly predicted based on past data.

Chaotic system:

A dynamical system the future of which can be predicted for short times, but due to the exponential growth of noise (“sensitive dependence on initial conditions”) long term prediction is not possible.

Random system:

A dynamical system the future of which cannot be predicted, based on past data.

Linear system:

Consider a dynamical system described in part by two variables (representing forces, displacements, or the like), one of which is viewed as input and the other as output. The part of the system so described is said to be linear if the output is a linear function of the input. Examples: (a) a spring is linear in a small force applied to the spring, if the displacement is small; (b) the Fourier transform (output) of a time series (input) is linear. Example (b) is connected with the myth that a linear transform is not useful for “linear data.” (To describe given time series data as linear is an abuse of the term. The concept of linearity cannot apply to data, but rather to a model or model class describing the data. In general given data can be equally well described by linear and nonlinear models.)

Phase portrait:

A picture of the evolution of a dynamical system, in a geometrical space related to the phase space of the system. This picture consists of a sampling of points tracing out the system trajectory over time.

Stationary system:

If the statistical descriptors of a dynamical system do not change with time, the system is said to be stationary. In practice, with finite data streams, the mathematical definitions of the various kinds of stationarity cannot be implemented, and one is forced to consider local or approximate stationarity.

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Books and Reviews

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Authors and Affiliations

  1. Space Science Division, NASA Ames Research Center, Moffett Field, USA

    Jeffrey D. Scargle

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    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Scargle, J.D. (2009). Astronomical Time Series, Complexity in. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_25

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