Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis and Lorenz equations. Credit not awarded for both MATH 5766 and MATH 3766. Prerequisites: Graduate student or Instructor permission. Cross-listed with: CSYS 5766.
Lectures
Day 1: Linear Systems, Logistic Map, [The Worldwide Air-Transportation Network]
Day 2: Fixed Point Classification
Day 3: Periodic Orbit Stability
Lecture 6: Sinks, Sources, and Saddles
Lecture 7: Linearization and the Jacobian
Lecture 9: Homoclinic Points
Lecture 10: Chaos
Core Concepts
Fixed Points and Stability
- Fixed Point Classification
- Attracting fixed point
- Repelling fixed point
- Saddle fixed point
- Banach Fixed Point Theorem