Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method

We consider quasi-periodic (with N basic frequencies) non-autonomousperturbations of Hamiltonian, reversible, volume preserving, and dissipativesystems. The unperturbed systems possess analytic families of invariantn-tori carrying conditionally periodic motions, are allowed to depend onexternal parameters, and are assumed to satisfy just very weak nondegeneracyconditions. We construct invariant $(n+N)$-tori in perturbed systems followingM.R. Herman's approach: additional external parameters are introduced toremove degeneracies and then are eliminated via an appropriatenumber-theoretical lemma concerning Diophantine approximations ofdependent quantities.