Math 145, Winter 1999: Chaos Theory

Lecture 2W, 13 Jan 1999

• Reminder of the rules: lab portfolios
• 2D flows:

  Where do 2D flows come from?

  Coupling two 1D flows in Stella

  A second order ODE in Stella

  State spaces: plane, cylinder, torus, sphere,...

  Rest points

  Attractor (focus, node), saddle, repellor

  The Characteristic Exponents (CEs)

  Attractors

  Points

  Cycles

  Separatrices

  Insets of saddles, repelling cycles

  Poincare section of a limit cycle

  Construction of the section

  Construction of the first return map

  The slope of the graph of the map

• Coming next: 2D bifurcations, 3D flows