ERRATA (as of March 18, 2019)
Imperfect Bifurcation in Structures and Materials —Engineering
Use of Group-Theoretic Bifurcation Theory, First Edition,Springer, 2002
by Kiyohiro Ikeda and Kazuo Murota
The following corrections should be made on the first edition of the book:• Page 21, Fig. 1.11: Should look

• Page 21, Fig. 1.12: Should look1

• Page 56, Footnote 4: Should read, being equal to the reciprocal of the coefficients in (2.70).
• Page 56, three lines below (2.71): Should read, When the condition of nondegeneracy (2.71) fails with “< 0,”• Page 57, the equation in the second line: Should read,b∂F= 2A200 w + A110 e
f + h.o.t. = ±(A110 2 − 4A200 A020 )1/2 ef + h.o.t.
∂w• Page 92, Eq. (4.33), “C” (in each of the three lines): Should read, “−C.”• Page 95, Eq. (4.37): Should read,
α1 + · · · + α5eϵ = −1.0577ϵ,fc ∼ Tξ (∂F/∂ f )0c• Page 103, the first line of Eq. (5.3): Should read, “C(d) = C0 a” instead of“C(d) = −C0 a.”• Page 104, the first line of Eq. (5.8): Should read, “ã” instead of “−ã.”• Page 157, Eq. (7.6): Should read,T (g)−T F(u, f ) = F(T (g)u, f ),g ∈ G.

(7.6)• Page 165, Eq. (7.28) and the paragraph thereafter: Should read,T (g)−T F(u, f, v) = F(T (g)u, f, S (g)v),

g ∈ G.

(7.28)

This looks slightly diﬀerent from (7.20) in that T (g) appearing on the left-handside of (7.20) is replaced by T (g)−T in (7.28). This diﬀerence, however, is not essential, since T (g)−T and T (g) are equal for a unitary representation T . Therefore,(7.28) can be rewritten in the form of (7.20) with a suitable basis change. See also
the argument in Remark 7.4.2.
• Page 184, Fig. 8.1: Should look2

• Page 191, (8.25): Should read,∗,nΣ(ξ(αi+bn j )) = Σ(η(αi+bn j )) = Din/b,ni = 1, . . . ,bn,

j = 0, 1,(8.25)

where the integer i∗ (1 ≤ i∗ ≤ n/bn) is determined from i by (i∗ −1)bj ≡ i−1 mod bn,
and∗

i,n,n
• Page 191, Dn/bin two places below (8.26): Should read, Din/b.
nn• Page 194, Fig. 8.4(a): Should look

• Page 211, the fifth displayed equation: Should read,e∂2 Uf + 3A2100 r2 + (−1)k−1 (bn − 1)A0,bn−1,00 rbn−2≈ A1010 e∂r22(−1)k−1 A0200 r
if bn = 3,
k−12b3[A+(−1)
A]rifn= 4,≈ 21000300
 3A r2if bn ≥ 5,2100
3

• Page 221, Line 3 in Remark 8.7.2: Should read, O(|ϵ|1/(bn−1) ), instead ofO(|ϵ|2/(bn−1) ).
• Page 234, Line 3 after (9.2): Should read, “and for all φ for bn ≥ 5.”• Page 236, two lines below (9.11): Should read, and τ̂(ψ) = τ̂(ψ; b) is anonlinear function in ψ and b = −A0300 /A2100 · · · .
• Page 241, the second line in subsubsection Case bn = 4: Should read, SinceC(d) is dependent on b = −A0300 /A2100 ,• Page 257, the first equation of (10.25): Should read, E[ζ] = −1.91,• Page 257, just below the displayed equation ζ = −τ̂(ψ)y: Should read, wherey = x1/3 and τ̂(ψ) = τ̂(ψ; b) with b = −A0300 /A2100 · · · .
• Page 270, Fig. 11.4: Should look

• Page 299, the first line of (12.15): Should read, {(+, ν2 , ν3 )Dnh | ν2 , ν3 = +, −}• Page 304, the last displayed equation: Should read,{2bnif bn is odd and ν = −,ň =bnif b
n is even or ν = +.
• Page 326, “Ω = {(x, y, z) ∈ R3 ” in Line 2: Should read, “Ω = {(x, y) ∈ R2 ”
• Page 327, the first equation and the next line in Remark 13.6.1: Should read,4

G′0 = ⟨σ x σy ⟩ ≃ D1 ,in which σ x σy represents ...

• Page 333, (13.31): Should read,mñ − m̃n,dmñ + m̃n±k =,d±k =±l ≡ mp + m̃ p̃ (mod d),±l ≡ mp − m̃ p̃ (mod d),(13.31)

where the double-signs correspond in each line of (13.31), and · · · .
• Page 355, the second to the last displayed equation: Should read,±k =mñ − m̃n,d±l ≡ mp + m̃ p̃ (mod d),where the double-sign corresponds, and · · · .
• Page 355, the last displayed equation: Should read,±k =mñ + m̃n,d±l ≡ mp − m̃ p̃ (mod d),where the double-sign corresponds, and · · · .
• Page 399, [122] in the reference list: Should read, Marsden, J.E. and Ratiu,T.S. instead of Ratiu, S.R.
• Page 403, [184] in the reference list: Should read, Vardoulakis, I. and Sulem,J. (1995), instead of (1992).

5