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Weakly mixing invariant tori of Hamiltonian systems. (English) Zbl 0945.37001

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.

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

Citations:

Zbl 0153.12602
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