Good books on Geometric Theory of Dynamical Systems I am looking for a good book on Geometric Theory of Dynamical Systems . I found Geometric Theory of Dynamical Systems by Jr. Palis myself,but it's very old, anyway i would like to find a  pure topological book about Dynamical systems.
On the other hand about:
local stability,
The kupka-Smale Theorm,
Genericity and stability of Morse-Smale Vector Field,
 A: Pick up (almost) anything by Ethan Akin. I particularly recommend "The General Topology of Dynamical Systems" available on Amazon. Although it is somewhat older than what you indicate you are looking for, he has many newer surveys on the subject that are downloadable on his website. 
In particular, the topological aspects of dynamics and stability are the main focus of his book and his survey articles. For instance, consider reading "Tourist's Guide to The General Topology of Dynamical Systems".
(PDF download link.)
A: A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems,  1997. 
M. Brin, G. Stuck, Introduction to Dynamical Systems, 2002. 
A: Such books are abundant. My favorite ones are Z. Nitecki, Differentiable dynamics,
and  J. Palis, W. de Melo, Geometric theory of dynamical systems. An introduction, Springer-Verlag, New York-Berlin, 1982. 
A: Take a look at Bob Easton's book Geometric Methods for Discrete Dynamical Systems'.
He was a student of Conley's, who took a very topological/geometric perspective. Conley's tiny monograph,Isolated Invariant Sets and the Morse Index' is also a gem
but perhaps too dense.
A: I guess "Geometrical Methods in the Theory of Ordinary Differential Equations" by Arnold should be in the list too, although it doesn't satisfy the "purely" topological criteria.
A: Mainly from the Hamiltonian point of view:
Zehnder: Lectures on Dynamical Systems 
