Math 145, Winter 1999: Chaos Theory

Lecture 4w, 27 Jan 1999

• review the bifurcation diagram for the logistic family
• the period doubling (or flip) bifurcation
• Theorem: there is exactly one attractor
• the case of r > 4: a chaotic repellor (like the Julia set)
• the definition of chaos
• the Cantor set
• symbolic dynamics, the shift
• periodic orbits, aperiodic dense orbit

• Devaney, 1985/1989, Sec. 1.5, p. 34