Dynamical systems and chaos (fys4190, spring 2008)

Time and place

Lectures
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
  1. Introduction, Flows, Fixpoints and Stability Analysis
    Background litterature:
    Week 3
    Strogatz, Chapters 1.0-3.5
    www.chaosbook.org, Chapter 2.

  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

  3. 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

  4. Chaos, Strange Attractors, Poincare Sections
    Background litterature:
    Week 8-9
    Strogatz, Chapter 9
    www.chaosbook.org , Chapter 3.

  5. Maps, Periodic Orbits, Kneading Sequences
    Week 10
    Background litterature :
    Strogatz, Chapter 10
    Lecture notes
    www.chaosbook.org, Chapter 5.

  6. 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

  7. Arnold Tongues, Mode Locking, Synchronization
    Background litterature:
    Week 15
    Strogatz
    Article: Transition to chaos by interaction of resonances in dissipative systems 1. circle maps

  8. Fractals and Multifractals
    Background litterature:
    Week 16
    Lecture notes
  9. 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 3
Strogatz: 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