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,
[Math] Good books on Geometric Theory of Dynamical Systems
differential-topologyds.dynamical-systemsgt.geometric-topologytextbook-recommendation
Best Answer
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.)