Self Study in Dynamical Systems

Good books with enough introductory material in this regard are:

1. introduction to dynamical systems, Michael Brin.

This book defines all the basic concepts of dynamic requirements of Chapter one is called Low dimensional dynamics Where does the topological classification of homeomorphisms of the circle (Theorem of Poincare). It also has the interesting theorem Sharkovsky (Generalization of period three implies chaos).

2.A First Course in Dynamics with a Panorama of Recent Developments.

This book covers a similar content, but with a different style of writing.

For books that go deeper into the core of the theory are two books by the same author:

1. Lectures on One-Dimensional Dynamics. Publ. do 17º Colóquio Brasileiro de Matemática, 1988

2. One Dimensional Dynamics. Springer-Verlag, 1993 With S. Van Strien

You can visit the author page: http://w3.impa.br/~demelo/listapub.html

Regarding prerequisites believe that in either case you need to know something of Differential Calculus.

When you want to discuss one-dimensional dynamic write to me.

Holmgren's "A First Course in Discrete Dynamical Systems" is very good written with simple worlds book. At the end of the book author gives list of books which are good continuation of one he wrote.

Check out math video lectures among other subjects on Chaotic Dynamical systems UCCS Math Video Lectures