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arXiv · 2507.12101

Singular KAM theory for convex Hamiltonian systems

Santiago Barbieri·Luca Biasco·Luigi Chierchia·Davide Zaccaria
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Abstract

In this note, we briefly discuss how singular KAM Theory - which was worked out in a previous work by L.B. and L.C. for the mechanical case $\frac12 |y|^2+\varepsilon f(x)$ - can be extended to convex real analytic nearly integrable Hamiltonian systems with Hamiltonian in action-angle variables given by $h(y)+\varepsilon f(x)$ with $h$ convex and generic $f$.

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Santiago Barbieri, Luca Biasco, Luigi Chierchia, Davide Zaccaria. 2025-07-16. Singular KAM theory for convex Hamiltonian systems. https://arxiv.org/abs/2507.12101

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