The aim of the course is to deal with the qualitative analysis of autonoumous
ordinary differential equations and to introduce to the theory of continuous and discrete dynamical systems. In particular the following basic concepts are studied: equilibrium, periodic orbit, homoclinic orbit, limit cycle, omega-limit set, invariance, conjugation and topological equivalence, Liapunov stability and asymptotic stability. Some of the well known examples of the literature are discussed. Among them: the fish, the conservative and the dissipative pendulum, the rotations on the circle and the quasi periodic motion on the torus. The student should reach the knowledge of the theory with reasonable depth, and also some working ability of the examples.
1. EXISTENCE AND UNIQUENESS.
2. LINEAR DYNAMICS.
3. FOUNDATIONS OF QUALITATIVE THEORIES.
4. INVARIANCE. LIMIT SETS.
6. LIAPUNOV STABILITY.
7. SUBGROUPS OF (R,+). PERIODS.
9. QUASI-PERIODIC MOTION ON THE TORUS.
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