I have enjoyed reading this detailed chapter. My only cons are that there is no discussion concerning structurally unstable, complex dynamics in "psuedo"-hyperbolic systems including ones with Lorenz attractors, homoclinic tangencies, etc, as well bifurcations separating Morse-Smale systems from other ones.
"...Singularities and closed orbits are hyperbolic..." By now, hyperbolicity was not yet introduced. Can an alternative way be used? like no characteristic exponents on the imaginary axis in case of equilibria, and no multipliers on a unit cycle in case of limit cycle?
Chaikin => Khaikin
The book was written by three authors: Andronov, Vitt and Khaikin. By the day it came out, Vitt had been sent to GULAG where he died. His name was forcefully removed from the first edition, but restored in the second and later editions.