The following is a list of the mathematically significant errata. Minor errata that do not affect the mathematical content, or that will be easily corrected by any reader, are not listed here. All of these errata have been corrected in the second printing (SIAM 1999).
Page 24: The coefficients in (1.3.10) should be 1/2 and 11/24 (not 2/3 and 19/27). This affects the table on page 25 and the whole discussion of this example.
Page 31: M=2/(2+ the rest)^3 (not 2 minus the rest).
Page 68: "Mantissa" should be "characteristic".
Page 103: K_3, not K_1, is assumed small.
Page 127 eq. (2.6.21): The order symbol in the denominator of lambda should be added at the end (not in the denomonator).
Page 144 new bottom: these conditions hold if a=1, b=2h>0, and 0<h<k. (Last condition should be added.)
Page 167, Fig. 4.3.1: The stable and unstable manifolds should cross transversally at the unstable rest point, rather than tangentially. Same in Fig. 4.3.3 page 170.
Page 207: Sixth line after (4.7.7b), square root of 8 delta_1 CUBED over 3 lambda_1.
Page 260 eq. (5.4.46): The b term should have a sine, not a cosine.
Page 262, ex. 7: omega^2-k^2=2 epsilon k omega_1 +...
Page 267: The argument for based on (5.5.20) is incorrect on this page and the next. Instead, the norm of R should be bounded by a sum of three terms, rather than two. The correct argument is given in the SIAM edition.
Page 278, eq. (6.1.8): The second equation should have a minus sign in front.
Page 290, Theorem 6.2.3: V must be convex (as well as compact) in order to get the Lipschitz condition.
Page 318: Theorem 6.5.2 is only true for stroboscopic averaging. Otherwise the initial conditions for the original and averaged solutions cannot be the same (but must be related via the averaging transformation). This also affects page 323 exercise 2.
Page 408: The rest point is at (2/3,-1), not -2/3. Same for the labeling of Fig. 7.8.1. (The figure itself is correct.)
Page 436 and 437: Planck (not Plank).
Page 458 eq. (9.4.4): The w equation should have a factor of y on the right-hand side.
Page 496 eq. (F.8): g'_i(t_i), not f''.