Moser and Smale-Birkhoff homoclinic theorems

Question

I have found in J. Moser "Stable and Random Motion in Dynamical Systems" the theorem about the topological conjugacy to the Bernoulli shift on a symbol space, and then again very well summarized and explained in S. Wiggins "Introduction to nonlinear dynamical systems and chaos". In the end, Wiggins states the Smale-Birkhoff homoclinic theorem, with some indications on the differences from Moser's theorem, without giving the proof. I was wondering if theres is and where i can find the proof of that theorem; i discovered the planar case in an article of Birkhoff, which is unfortunately unfindable, and the general case from Smale's article "Diffeomorphisms with many periodic points", which requires more topological background respect to how it is stated in Wiggins' book. Any advice? Thanks in advance.

Answer 1

For diffeomorphisms, the Birkhoff-Smale theorem is well explained in the book of Robinson, Dynamical systems, stability, symbolic dynamics and chaos.