Code
Φ-408
Level
Undergraduate
Category
C
Teacher
N. Lazaridis
ECTS
6
Hours
3
Semester
Spring
Display
No
Offered
No
Goal of the course
The 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).
Program
Wednesday, 11:00-13:00, Room 2
Thursday, 11:00-13:00, Room 2
Thursday, 11:00-13:00, Room 2
Syllabus
1. 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.
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.
"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.
