Laskar's frequency map analysis revisited

arXiv:2608.02182 · math.DS, astro-ph.EP, math-ph · Submitted 2026-08-03 · Read on arXiv

Zhicheng Tong, Yong Li

math.DS, astro-ph.EP, math-ph

Submitted: 2026-08-03

Comments: Any comments are welcome!

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Aperture — 2× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes

Sources

• Frequency map analysis and quasiperiodic decompositions
• Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity
• Towards sharp regularity: Full-dimensional tori in $ C^\infty $ vector fields over $ \mathbb{T}^\infty $
• Weighted multiple ergodic averages via analytic observables over $ \mathbb{T}^\infty $: Is exponential pointwise convergence universal?
• Optimal rates of uniform convergence for weighted Birkhoff averages via almost all rotations
• Identification of MHD equilibrium $\beta$ limits for CFQS plasmas

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