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The reversible context 2 in KAM theory: the first steps. (English) Zbl 1277.37091

Summary: The reversible context 2 in KAM theory refers to the situation where \(\dim \, \text{Fix} \, G < \tfrac 1/2 \, \text{codim} \mathcal{T}\), here \(\text{Fix} \, G\) is the fixed point manifold of the reversing involution \(G\) and \(\mathcal{T}\) is the invariant torus one deals with. Up to now, this context has been entirely unexplored. We obtain a first result on the persistence of invariant tori in the reversible context 2 (for the particular case where \(\dim \, \text{Fix} \, G = 0\)) using J. Moser’s modifying terms theorem of [Math. Ann. 169, 136–176 (1967; Zbl 0149.29903)].

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
70K43 Quasi-periodic motions and invariant tori for nonlinear problems in mechanics

Citations:

Zbl 0149.29903
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