Erratum: Fenichel theory for multiple time scale singular perturbation problems (SIAM Journal on Applied Dynamical Systems (2017) 16 (1425-1452) - Cardin, Pedro Toniol [UNESP]; Teixeira, Marco Antonio (Society for Industrial & Applied Mathematics (SIAM), 2019)
On p. 1432 of [1], hypothesis (H) should have been written as follows: (H) If L1 ⊂ M1 is a compact submanifold, we assume that the matrix Dx1f1(x0; 0) has no eigenvalues with zero real part for all x0 2 L. And for each k = 2; : : : ; n - 1, if Lk ⊂ Mk is a compact submanifold, we assume that the matrix Dxk ~ fk(x0; 0) has no eigenvalues with zero real part for all x0 2 Lk, where ~ fk is the restriction of fk to Mk⊂1. Despite the new wording, the results and their proofs are not a ected. Moreover, the interpretation of this hypothesis remains unchanged, that is, the submanifold Lk of Mk, as a set of equilibria of the limiting problem (Pk), is normally hyperbolic relative to (Pk) for k = 1; : : : ; n - 1. Note that for k = 2; : : : ; n - 1, the limiting problem (Pk) is de ned on the manifold Mk⊂1, so that we must consider the restriction ~ fk of fk to Mk⊂1 (and not fk properly) and assume that Dxk ~ fk(x0; 0) (instead of Dxkfk(x0; 0)) has no eigenvalues with zero real part.