Introduction to Dynamical Systems - Part 1/2 (J. Fejoz)
1. Bibliography
- M. Brin and G. Stuck, Introduction to Dynamical Systems, 2002 (PDF file)
A good part of the material of the first part of the course is contained in the first chapter of this book. - V. Arnold, Ordinary Differential Equations, 1992 (DJVU file)
Excellent introductory book on ODEs - V. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, 1988 (DJVU file)
Advanced book with a wealth of topics studied. A jewel! - V. Arnold, Mathematical Methods of Classical Mechanics, 1989 (DJVU file)
- J. Milnor, Morse Theory, 1969 (PDF file)
2. Calendar
- September 15
- Notion of dynamical system. Conjugacy. Example of the pendulum
- September 22
- First classification of rotations of the circle. An expanding endomorphism of the circle. Semi-conjugacy to the Bernoulli shift
- September 29
- A hyperbolic toral automorphism 1/2. Structural stability
- October 6
- A hyperbolic toral automorphism 2/2. Topological entropy.
Definitions of being topologically transitive or mixing, ergodic and mixing. - October 13
- Introduction to Hamiltonian systems
- October 20
- Introduction to KAM theory