The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces

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The parameterization method for invariant manifolds II: regularity with respect to parameters (2002, methodology): “1 of [1] has derivatives Da λD b xK for each (a, b) in the same set Σi,j .”
The parameterization method for invariant manifolds III: overview and applications (2003, methodology): “This remark played an important role in [Ste57] and, more explicitly in [BdlLW96] and [CFdlL03a].”
Computation of maximal local (un)stable manifold patches by the parameterization method (2015, methodology): “We also note that if there is a resonance then the invariance equation can be modified so that we conjugate to a polynomial (instead of linear) dynamical system [5, 44], and that the later work just cited implements computer assisted error bounds for the resonant case using the radii polynomial appr”