EIC2107 – Dynamical Systems Physics

I taught this second-year course from the Bachelors program in Informatics and Computing Engineering during the time that it was offered, between 2004 and 2006. When the Bachelors program was replaced by an Integrated Masters program, this course was not offered anymore.

Objectives

Studying some contemporary topics on dynamics. Learning how to use a Computer Algebra System (CAS). Studying applications of dynamical systems in various fields using a practical approach.

Program

1. Discrete dynamical systems. First and second order systems. Fixed points and cycles. Bifurcations and chaos. Random systems. Iterative Function Systems (IFS). L systems.
2. Continuous dynamical systems. Phase space. Direction fields. Numerical solution of differential equations. Analytical methods.
3. Linear and non-linear systems. Linearization. Stability and bifurcations. Predator-prey systems. Limit cycles. Chaos.
4. Hamiltonian systems. Linear and non-linear oscillators. Self-controlled oscillations.
5. Discrete systems on the complex plane. Newton's method. Julia and Mandelbrot sets.

Bibliography

• Villate, J. E. (2007). Introdução aos sistemas dinâmicos: uma abordagem prática com Maxima. Porto, Portugal: author's edition. ISBN: 9729939608. DOI: 10.24840/978-972-99396-0-8.
• Acheson, D. (1997). From calculus to chaos. An introduction to dynamics, Oxford University Press.
• Blanchard, P., Devaney, R. L. & Hall, G. R. (1999). Ecuaciones diferenciales, International Thomson Editores.
• Devaney, R. L. (1992). A first course in chaotic dynamical systems: theory and experiments, Westview Press.
• Garcia, A. L. (2000). Numerical methods for physics, Prentice-Hall.
• Peitgen, H.-O., Jurgens, H. & Saupe, D. (1992). Chaos and fractals: new frontiers of science, Springer-Verlag.
• Redfern, D., Chandler, E. & Fell, R. N. (1997), Macsyma ODE lab book, Jones and Bartlett Publishers, Boston.