Math 443, Section C1; Fall Semester 1998
Ordinary Differential Equations

Professor:
Eugene Lerman
334 Illini Hall
2449510
lerman@math.uiuc.edu, URL https://math.uiuc.edu/~lerman/

Class Time/Place:
MWF 10 343 Altgeld

Prerequisites:
Undergraduate analysis or a smattering
of topology of metric spaces.

Text:
No text required. Recommended text:
P. Glendinning Stability, Instability and Chaos.
An Introduction to the Theory of Nonlinear Differential Equations.
Syllabus:
 1.
 Introduction:
 phase spaces, vector fields and flows;
 existence and uniqueness theorems
 limit sets
 2.
 Stability: various notions of stability, Liapunov functions
 3.
 Linear differential equations
 exponentiation of operators
 real and complex Jordan normal forms of matrices, autonomous
linear ODEs.
 Floquet theory
 4.
 Linearization and hyperbolicity
 linearization
 stable manifold theorem
 HartmanGrobman theorem
 5.
 Dynamics in two dimensions
 Poincaré index
 Bendixon and Dulac criteria
 PoincaréBendixon theorem
 6.
 Periodic orbits and Poincaré maps
 Poincaré maps
 structural stability, genericity, transversality
 7.
 Bifurcation theory
 center manifold theorem
 the saddle node bifurcation
 the pitchfork bifurcation
 the PoincaréAndronovHopf bifurcation
last changed 5/8/1998