Knill, Oliver Weakly mixing invariant tori of Hamiltonian systems. (English) Zbl 0945.37001 Commun. Math. Phys. 204, No. 1, 85-88 (1999). The author proves the theorem: Given a real analytic Hamiltonian \(H\) for which there exists an invariant torus \(N\) on which the dynamics is quasi-periodic, there exists a Hamiltonian \(K\) arbitrarily close to \(H\) for which the same torus is still invariant and for which the dynamics on \(N\) is ergodic and weakly mixing. Reviewer: Lev Lerman (Berlin) MSC: 37A25 Ergodicity, mixing, rates of mixing 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion Keywords:invariant torus; weakly mixing; Hamiltonian; Shklover’s theorem Citations:Zbl 0153.12602 PDFBibTeX XMLCite \textit{O. Knill}, Commun. Math. Phys. 204, No. 1, 85--88 (1999; Zbl 0945.37001) Full Text: DOI