Abstract
In this paper, we consider certain mappings, \({\mathcal {M}}\) , sufficiently close to an integrable one, which is weakly reversible with respct to the mappings \({\mathcal {G}}\) sufficiently close to an involution of tye (m, n), where m, n∈Z + are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for providing the existence of a Cantor family of m-tori invariant under the reversible mappings \({\mathcal {M}}\) and the reversing mapping \({\mathcal {G}}\).
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