DYNAMICAL SYSTEMS

1. To give the base elements of continuous and discrete dynamical systems

2. Starting from the real world models to build mathematical models.

3. Analysis and interpretation of the results.

4. Study of the dynamic flow systems: equilibria and their stability, attractors.

Introduction to discrete and continuous finite-dimensional dynamical systems.

Linear and nonlinear dynamical systems

Equilibria and their stability

Periodicity and chaos

Fractals

Complete programme here:

http://www.dmi.unict.it/~mulone/programma_sistemidinamici1617.pdf

1. E. Scheinerman, Invitation to Dynamical Systems, testo disponibile online: http://www.ams.jhu.edu/∼ers/invite/book.pdf

2. L. Perko, Differential equations and dynamical systems, 3rd ed. - New York: Springer-Verlag, 2001.

3. M. W. Hirsch, S. Smale, Differential equations, dynamical systems, and linear algebra, New York: Academic Press, 1974.

4 E. Salinelli, F. Tomarelli, Modelli dinamici discreti, Milano: Springer-Verlag Italia, 2002.

5. S.H. Strogatz, Nonlinear dynamics and caos, Westview, Cambridge, MA, 2000.

6. A. Milani comparetti, Introduzione ai sistemi dinamici, Ed. Plus, Pisa, 2002

7. S. Lynch, Dynamical Systems with Applications using MATLAB, Birkh¨auser 2004.

8. G. Mulone, Appunti di sistemi dinamici, 2002.