| TFYY02 | Chaos and non-linear phenomena, ECTS-points /Kaos och icke-linjära fenomen/ Advancement level: D | |
| Aim: Kursen är avsedd att ge dels en orientering om de speciella egenskaperna hos icke-linjära system av ingenjörsmässigt intresse, samt också ge en orientering om några aktuella forskningsområden såsom solitoner och ``breathers''. Prerequisites: TFFY17 Modern Physics, TFFY02 Mathematical Methods of Physics or TATM 58, Partial Differential Equations, FFFY 43 Analytical Mechanics. The courses TFFY54 Quantum Mechanics and TFFY70 Physics of Condensed Matter part I are recommended. Course organization: 38 hourse lectures and 18 hours exercises solving problems. Course content: Introduction. Experiments and simple models. Vibrations in mecanical systems and electrical circuits. Piesewise linear maps and deterministic chaos. Universal behavior of quadratic maps. Bifurcations. Poincare maps. Lyapunov exponents. Fractal dimensions. Period-doubling. Homoclinic and heteroclinic orbits. The intermittency route to chaos. Strange attractors in dissipative dynamical systems. The transition from quasiperiodicity to chaos. Regular and irregular motion of conservative systems. Integrable and non-integrable systems. Solitons with applications and breathers. Chaos in quantum systems. Course literature: To be determined later. | ||
| TEN1 | Homework problems. | |