KAM theory, Arnold diffusion and long-term stability
Nearly regular motion such as planetary orbits is kept in order by invariant tori found by Kolmogorov, Arnold and Moser (KAM theory), but with three or more degrees of freedom orbits can slowly drift through the gaps between tori (Arnold diffusion). How general this drift is, and how fast it acts, is not settled.
Why it matters
It decides the long-term predictability of nearly integrable systems, from the solar system to particle accelerators and magnetic confinement.
Review
V. Kaloshin, K. Zhang, Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom, Annals of Mathematics Studies 208, Princeton University Press, 2020. https://doi.org/10.23943/princeton/9780691202525.001.0001 reference checked
See also
Timestamp record
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- Public log
- Entry 261, in checkpoint 2,123
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- Block 969,698, 2026-10-03
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