Here you can find lists of great Dynamical Systems books are or have been used to teach courses at Caltech.
By: Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
By: Yakov Pesin and Vaughn Climenhaga
By: Steven H. Strogatz
By: Lawrence Perko
By: John Guckenheimer, Philip Holmes
By: Morris W. Hirsch, Stephen Smale, Robert L. Devaney
By: Ferdinand Verhulst