Dynamical systems and chaos (fys4190, spring 2008)
Time and placeLectures
Jan14 - Mar 24 and Apr 7. - May 26.
Monday: 13:00 -14:00, PGP, Fysikkbygningen
Tutorial lectures
Friday : 09:15 -12:00,PGP seminar room, Fysikkbygningen
Tentative plan
- Introduction, Flows, Fixpoints and Stability Analysis
Background litterature:
Week 3
Strogatz, Chapters 1.0-3.5
www.chaosbook.org, Chapter 2.
- Bifurcations, Saddle node, Transcritical, Pitchfork and Hopf
Background litterature :
Week 4
Strogatz, Chapters 4.1-6.3
www.chaosbook.org, Chapter 4.
Week 5
Strogatz, Chapters 6.3-6.8
- Limit Cycles, Perturbation Analysis of Two-timing
Background litterature :
Week 6
Strogatz, Chapters 7.0-7.6
Week 7
Strogatz, Chapters 8.0-8.5
- Chaos, Strange Attractors, Poincare Sections
Background litterature:
Week 8-9
Strogatz, Chapter 9
www.chaosbook.org , Chapter 3. - Maps, Periodic Orbits, Kneading Sequences
Week 10
Background litterature :
Strogatz, Chapter 10
Lecture notes
www.chaosbook.org, Chapter 5.
- Period Doubling, Feigenbaum and Libchaber, Renormalization
Background litterature:
Week 11-14
www.chaosbook.org, Chapter 10-12.
Strogatz, Chapter 10
Article: Quantitative universality for a class of nonlinear transformations
- Arnold Tongues, Mode Locking, Synchronization
Background litterature:
Week 15
Strogatz
Article: Transition to chaos by interaction of resonances in dissipative systems 1. circle maps
- Fractals and Multifractals
Background litterature:
Week 16
Lecture notes
General background and introductory material will be found in,
Steven H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering.
Problems
Week 3Strogatz: 2.5.6, 2.6.1, 2.6.2, 3.2.5, 3.2.6
Week 4 (pdf)
Week 5
Strogatz: 6.5.19, 6.6.8, 6.8.2-6.8.5, 6.8.14
Week 6 (pdf)
Week 7
Strogatz: 8.1.10, 8.3.1, 8.5.3, 8.4.3
Week 8-9
Rossler Attractor
Week 10-
Project