Course Lectures: highlighted/underlined materials are in pdf format.

• Week 1: Read [Verhulst] sections 9.1-9.4, and 10.1-10.2.
  • lecture 1A Course overview.
  • lecture 1B Introduction to perturbation theory.
  
  
• Week 2: Read [Verhulst] sections 10.3-10.4 ( and [Perko] section 3.5, optional).
  • lecture 2A The Poincare-Lindstedt method and the computation of periodic orbits.
  • lecture 2B Application to space mission design: the computation of a halo orbit and its invariant manifolds.
  
  
• Week 3: Read [Verhulst] 11.1-11.5, and 11.8.
  • lecture 3A The method of averaging.
  • lecture 3B The method of averaging. II.
  
  
• Week 4: Read [Wiggins] chapter 18 and section 19.1.
  • lecture 4A Center manifolds. Introduction to bifurcation theory.
  • lecture 4B Normal form theory.
  
  
• Week 5: Read [Wiggins] section 19.2 and sections 20.1-20.2.
  • Normal forms.
  • lecture 5B Final project introduction
  
  
• Week 6: Read [Wiggins] chapters 23 and 24.
  • Bifurcation of equilibrium solutions and Hopf bifurcation.
  • Introduction to chaos: symbolic dynamics, Smale horseshoe, Conley-Moser conditions, and homoclinic and heteroclinic dynamics.
  
  
• Week 7: Read [Wiggins] chapters 25 and 26.
  • Introduction to Melnikov method.
  • The chaotic dynamics in the restricted three-body problem and its application to mission design.
  
  
• Week 8: Read [Verhulst] sections 15.1-15.4.
  • Introduction to Hamiltonian systems.
  • Birkhoff normalization. The phenomenon of recurrence.
  
  
• Week 9: Read [Verhulst] sections 15.5-15.8.
  • Periodic solutions. Invariant tori and chaos. The KAM theorem.
  
  
• Week 10: Introduction to chaotic transport theory. Its application in dynamical astronomy, space mission design, and fluid mechanics.

CDS 140b