Courses Catalogue

Syllabus of the course: Dynamical Systems


In this web page we provide the syllabus of the course Dynamical Systems, offered by the Department of Physics.
The list of the courses offered during the current accademic year is available here.
The list of all courses offered by the Department of Physics is available here.

CodeΦ-408
TypeC
ECTS6
Hours3
SemesterSpring
InstructorN. Lazaridis
ProgramWednesday, 11:00-13:00, Room 2
Thursday, 11:00-13:00, Room 2
Web page
Goal of the courseThe goal of the course is to introduce fourth year physics students to various concepts of Dynamical Systems and Chaos, and the methods used for their analysis. It is recommended that the students have passed the courses of Classical Mechanics I (Φ-204) and Quantum Mechanics I (Φ-303).
Syllabus1. Introduction. General introduction to the concepts of dynamical systems, nonlinearity, and chaos.
2. Nonlinear differential equations. Phase space, equilibrium points, stability and bifurcations.
3. Integration of differential equations. Integrable and non­integral systems,first integral, time­dependent integrals, numerical integration.
4. Perturbation theory. Poincare ­ Linstedt method, the method of multiple time­scales, singular perturbations.
5. Chaos in Hamiltonian systems. Simple systems that exhibit chaotic behavior, from differential equations to maps, area preserving maps, homoclinic and heteroclinic orbits.
6. Dynamics of dissipative systems. Transitions to chaos, dissipation and turbulent flow, strange attractors.
7. Characterization of chaotic attractors. Attractor dimension, Lyapunov exponents and hyperchaos, topological entropy, power spectra.
8. Quantum chaos and integrability. WKB method, semiclassical quantization, spectra, quantum maps.
Bibliography "Introduction to nonlinear science", G. Nicolis, Cambridge University Press, Cambridge, 1995.
"Chaotic Dynamics", T. Tel and M. Gruiz, Cambridge University Press, New York, 2006.
"Nonlinear Ordinary Differential Equations", D. W. Jordan and P. Smith, Oxford University Press, New York, 1987.

University of Crete - Department of Physics - P.O Box 2208 - GR-71003 Heraklion, Greece
phone: +30 2810 394300 - fax: +30 2810 394301