| Abstract: |
| In this talk we present an a-posteriori KAM theorem for the existence of Lagrangian invariant tori in Hamiltonian systems of $n$ degrees of freedom with $(n-d)$ first independent integrals in involution that induce a Hamiltonian action of the $(n-d)$-dimensional torus. We present a (modified) quasi-Newton method for the invariance equation of the torus parameterization, whose convergence from an initial approximation, and under appropriate non-degeneracy conditions, leads to the proof of the result with optimal estimates. The approach is suitable for developing numerical algorithms and performing computer-assisted proofs. |
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