The author is a very good mathematician (and a grandfather of Google) so I was expecting a short and lucid introduction to dynamical system. Imagine my sadness when I found the book barely comprehensible. Apparently, the author learned his writing skills in Russian in the 60s, where paper was scarce, and any sort of explanation was viewed a waste thereof. If you actually want to understand dynamics, Katok/Hasselblatt Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications) is vastly superior.