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Chaos theory in geophysics: past, present and future. (English) Zbl 1080.37610

The author suggests the usefulness of the ideas of the chaos theory in understanding geophysical phenomena. Through a systematic review of chaos theory applications in geophysics, with particular reference to the geophysical phenomena studied, promising results achieved and lessons learned, and potential areas for improvements, the author presents further support to such case. His analysis, based on the arguments that he himself put forth, is that “chaos theory” should not be viewed as a separate theory, but rather as a theory that “connects” both “deterministic” and “stochastic” theories, taking into account the advantages of the two theories as well as their limitations. The author believes that the ideas of chaos theory have immense potential in geophysics, even in the fields and problems not discussed in this article, and hopes that in the coming years and decades of this century would witness proof to such a belief.

MSC:

37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
86A04 General questions in geophysics
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