Articles | Volume 30, issue 4
Review article
05 Oct 2023
Review article |  | 05 Oct 2023

Review article: Dynamical systems, algebraic topology and the climate sciences

Michael Ghil and Denisse Sciamarella

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Orbital insolation variations, intrinsic climate variability, and Quaternary glaciations
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Abrupt climate changes and the astronomical theory: are they related?
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Preprint withdrawn
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Dansgaard–Oeschger-like events of the penultimate climate cycle: the loess point of view
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Related subject area

Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Variational techniques for a one-dimensional energy balance model
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Sensitivity of the polar boundary layer to transient phenomena
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Existence and influence of mixed states in a model of vegetation patterns
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Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
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Cited articles

Abarbanel, H. D. I. and Kennel, M. B.: Local false nearest neighbors and dynamical dimensions from observed chaotic data, Phys. Rev. E, 47, 3057–3068,, 1993. a
Aguirre, L. A., Letellier, C., and Maquet, J.: Forecasting the time series of sunspot numbers, Solar Phys., 249, 103–120, 2008. a
Amon, A. and Lefranc, M.: Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator, Phys. Rev. Lett., 92, 094101,, 2004. a
Arnold, L.: Random Dynamical Systems, Springer-Verlag, New York/Berlin, 1998. a
Arnol'd, V. I.: Geometrical Methods in the Theory of Ordinary Differential Equations, Springer Science & Business Media; first Russian edition 1978, 2012. a, b, c
Short summary
The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.