Differentiable dynamical systems. An introduction to structural stability and hyperbolicity (Q2816591)

This is a graduate textbook on the abstract theory of differentiable dynamical systems which focuses mainly on structural stability and on hyperbolicity which plays a basic role in this topic. This is a book for mathematicians, which discards physical applications, but involves many theoretical exercises for solving, at the end of each chapter. The book begins with the basics of dynamical systems and then goes on with hyperbolic fixed point, Smale horseshoe, hyperbolic sets, Axiom A and quasi-hyperbolicity versus linear transversality. The key word is homeomorphism. The book is quite suitable for what it intends to do and what it intends to be.