4.0 A better way to understand Differential Equations | Nonlinear Dynamics | Index Theory

Series1:
Part 1:    • 1.0 A better way to understand Differ...  
Part 2:    • 2.0 A better way to understand Differ...  
Part 3:    • 3.0 A better way to understand Differ...  

Index theory is a method used to gain global information about a nonlinear differential equation. One powerful insight is that closed orbits (periodic solutions) must have at least one fixed point inside of the curve. In fact, for a periodic orbit, there must be 1 more fixed point of index = +1 than saddle fixed points.

Chapters:
0:00 Last time
0:48 Intro
0:58 Motivation
2:04 Index of Closed Orbits
3:53 Index Examples
6:02 Defining Phi and Index
8:18 Proof Index Integer
8:47 Proof Index Constant Under Deformation
10:24 Index of Fixed Points
10:49 Index of Multiple Fixed Points
12:38 Index Closed Orbits = +1
13:00 Examples Closed Orbits
13:53 Ruling Out Closed Orbits
14:13 Next time
14:32 Outro

Music: Go Season by Milano
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