English

Singular KAM theory for convex Hamiltonian systems

Dynamical Systems 2025-07-17 v1

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 12y2+εf(x)\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)+εf(x)h(y)+\varepsilon f(x) with hh convex and generic ff.

Keywords

Cite

@article{arxiv.2507.12101,
  title  = {Singular KAM theory for convex Hamiltonian systems},
  author = {Santiago Barbieri and Luca Biasco and Luigi Chierchia and Davide Zaccaria},
  journal= {arXiv preprint arXiv:2507.12101},
  year   = {2025}
}
R2 v1 2026-07-01T04:03:57.756Z