Ordinary Differential Equations II

Department: 
MATH
Course Number: 
6308
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Usually every spring semester

This sequence develops the qualitative theory for systems of differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. (2nd of two courses)

Prerequisites: 

MATH 6307

Course Text: 

No text

Topic Outline: 
  • Normal Forms Poincare's theorem, Siegel's theorem, periodic coefficients, Hamiltonian systems
  • Mappings Logistic map, circle maps, rotation numbers, Denjoy theorem
  • Elementary Properties of Chaos Smale horseshoe, transverse homoclinic orbits, exponential dichotomies, homoclinic saddle focus, chaotic attractors, entropy, Liapunov exponents
  • Nonautonomous Systems Bounded and quasiperiodic solutions, averaging, invariant tori, skew product flows