Errata and Other Infelicities in the Text
DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS.
- Page xiv, line 1: I would like to thank... should be We
like to thank...
- Page 4, line 16: increase without bound
- Page 13, line 10 (and elsewhere on this page):
The partial of f with respect to x0 is really
the partial of f with respect to the "variable" phi.
- Page 27, last line should read: That is, two nonzero
vectors V and W...
- Page 38, Exercise 13 should read: A( alpha V1 +
beta V2) = alpha A V1 + beta A V2
- Page 58, very interesting way to enumerate the phase portraits in
Figure 3.9, don't you think?
- Page 59, Exercise 9 should read complex eigenvalues with nonzero
- Page 66: Note that, in the proof of the Theorem, the "only if" part is
missing. This part
follows immediately, however, from the assertion at the top of
page 66 regarding the fact that, if the eigenvalues are negative, then the
conjugacy takes curves tending to the equilibrium point to other such curves.
So if there is only one negative eigenvalue, then we only get a single curve
of such solutions, but if there are two eigenvalues with negative real parts,
we get a whole open set of such solutions and so there is no conjugacy.
- Page 86, last line: first component of V should be
x1 + iy1.
- Page 88, line 18 Section 5.1, not 5.2.
- Page 88, last line: W2j should be
- Page 102. Fifth line of the proof should read "Since
V2 is open...".
- Page 111, line 3: in the k1 component of the solution
replace ck with ck1.
- Page 116. In the general solution Y(t) at the bottom of the page,
the terms yi(t) should each be multiplied by
- Page 118: The formulas for theta1 and
theta2 are wrong, they should
read theta1 = theta1(0) -
omega1(t), a minus sign rather than a
plus sign in each of these cases. This does not affect the Poincare
- Page 144, Equation 3 (as well as just above) should read:
uk+1(t) instead of
ur+1(t). Similarly, uk(s) instead of
ur(s). Most importantly, inside the integral should
read F(uk(s)), not just uk(s).
- Page 147. Remove the first K in the Theorem.
- Page 164, last equation: theta' should be 1, not
- Page 169, line 11: hs(y) should be
- Page 177, line 13: The bifurcation should have gone "the other
way", i.e., with a < a0.
- Page 178, line 3: The second term in the numerator should be
GxGxa, but of course this does not change
anything since this entire term is zero because Gx = 0
- Page 192, line 6: x + or - 1 should read x = + or
-1, the equals sign is missing.
- Page 195, the example: Technically, we have not shown that linearization
implies that the origin is unstable when epsilon > 0. However, this
follows immediately from the fact that the x, y-plane is invariant and
the system is actually linear on this plane for all epsilon.
- Page 196, line 2 and line 6: L' should be L'/2.
- Page 204, line -6: the words "isolated minimum" should be
replaced by "isolated critical point that is a minimum."
- Page 242 line -10: The proof follows from Corollary 5 in 10.6, not
- Page 251 line -10: The expression xMx +
yMy should read xMx +
- Page 251 line -3: lies over mu should read to the left of nu.
- Page 295 last line: v_theta should be u_r
- Page 297, Exploration 13.8: The potential energy U(X) should be
the negative of what is written, i.e., U(X) = -1 / |X|^v.
- Page 326, problem 9: This problem should read "show that the system is
not chaotic in the region where x, y, and z are all positive."
- Page 332, figure 15.4: The labels of the graphs should be y =
f(x) and y = f2(x) instead of y =
xf(x) and y = xf2(x)
- Page 333, figure 15.5: The captions should read fc(x)
rather than fc(x). Also, there is a missing parenthesis in
the first displayed equation.
- Page 335, figure 15.6: The captions should read fc(x)
rather than fc(x).
- Page 337, figure 15.7: In the caption the minus sign should be an equals
- Page 347, line 19: tn+1 should be
- Page 348, line -4: the superscripts should be n+1, not n.
- Page 379. The third equation in the Chua circuit system should
read z' = - by, not -bz.
Special thanks to the following people for catching the above errors:
- Jamil Abreu
- Larry Baker
- Jeff Haag and his students at Humboldt State
- Kresimir Josic and his students at the University of Houston
- John Josef Leth
- Benjamin Lotto
- Tiennyu Ma
- Luis Fernando Mello
- Bogdan Przeradzki
- Charles Pugh
- Jeffrey Rabin
- Martin Raussen
- Julian Wilson